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Solved Examples
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DD  Use Pythagorean theorem to find the length of BC¯.
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DD  Use Pythagorean theorem to find the length of RQ¯.
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DD  Use Pythagorean theorem to find the length of AC¯.
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DD  Use Pythagorean theorem to find the length of BC¯.
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DD  If a = 4.5 units and b = 6 units, then find the measure of the hypotenuse in the right triangle.  DD View Solution
DD  Figure ABCD is a rectangular field 68 ft long and 51 ft wide. By how much is the path from A to C shorter than the path from A to B to C?  DD View Solution
DD  The length of the chord AB = 12 in. Find the radius of the circle O.
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DD  If a = 25.6 units and c = 54.4 units, then find the value of b in the figure.  DD View Solution
DD  If b = 20.4 units and c = 25.5 units, then find the value of a in the figure.  DD View Solution
DD  If b = 27 cm and c = 9 cm, then find the value of x in the right triangle.
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DD  Find the value of x in the figure. [Given b = 5.1 units, and a = 0.85 units.]  DD View Solution
DD  One side of a right triangle is 15 ft and the length of its hypotenuse is 25 ft. Find the length of the other side.
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DD  Find the length of the altitude BC¯ of triangle ABC if x = 5 and y = 3.
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DD  Find all the side measures of the right triangle. [Given a = 6x, b = 9x - 3 and c = 9x + 3.]  DD View Solution
DD  What is the diameter of the circle with center O, if AC = 4 in and AB = 5 in?  DD View Solution
DD  One leg of a right triangle is 15 inches long. The other leg is 3 inches less than the hypotenuse. What are the lengths of this leg and hypotenuse?
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DD  Josh walked diagonally across a square garden with each side measuring 20 ft long (from one corner to the opposite corner). How far did he walk?
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DD  The radius of the circle is 6 in. Find the length of the sides of the square.
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DD  The perimeter of a right triangle is 180 inches and the ratio of the lengths of the 2 legs is 5 : 12. Find the length of the hypotenuse.
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DD  The lengths of hypotenuse and shorter leg of a right triangle are in the ratio 5 : 3 and the perimeter of the triangle 108 inches. Find the length of the longer leg.
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DD  Diameter of the circle O is 14 cm. Find the length of the chord AC.
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DD  The radius of the circle is 19.5 cm. The perpendicular distance from the center of the circle to the chord is 11.7 cm. Find the length of the chord PQ.
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DD  A ladder which is 25 ft long is placed on a wall such that the top of the ladder touches the top of the wall. The bottom of the ladder is 15 ft away from the wall. What is the height of the wall?
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B   One leg of a right triangle is 5 in. less than the other leg. The length of the hypotenuse is 25 in. Find the lengths of the legs.
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B   What is the length of the third side of the triangle shown in the figure?[Given a = 9.6 cm and b = 12.8 cm .]   B View Solution
B   Shethal went to a level field to fly a kite. She let out all 195 ft of string and tied it to a stake. Then she walked out on the field until she was directly under the kite, 117 ft from the stake. How high was the kite?   B View Solution
B   The hypotenuse of a right triangle is 4 feet more than its longer leg. The length of shorter leg is 12 feet. Find the length of the longer leg and hypotenuse.
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B   One end of a 15 feet long wire is tied to the top of a pole and the other end is fixed on to the ground at a distance of 9 feet from the foot of the pole. What is the height of the pole?   B View Solution
B   The perimeter of a right triangle is 48 units. The sum of the squares of all the sides is 800 sq.units. What is the area of the triangle?   B View Solution
B   P is a point in the interior of the rectangle ABCD. AP = 21 units, CP = 12 units and DP = 13 units. What is the value of BP¯?   B View Solution
B   One leg of a right triangle is 21 inches long. The other leg is 5 inches less than the hypotenuse. What are the lengths of this leg and hypotenuse?
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B   If a = 6.6 units and b = 8.8 units, then find the measure of the hypotenuse in the right triangle.   B View Solution
B   The radius of the circle is 5 in. Find the length of the sides of the square.
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B   Diameter of the circle O is 22 cm. Find the length of the chord AC.
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B   A ladder which is 20 ft long is placed on a wall such that the top of the ladder touches the top of the wall. The bottom of the ladder is 12 ft away from the wall. What is the height of the wall?
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B   Shethal went to a level field to fly a kite. She let out all 230 ft of string and tied it to a stake. Then she walked out on the field until she was directly under the kite, 138 ft from the stake. How high was the kite?   B View Solution
B   Use Pythagorean theorem to find the length of RT¯.
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B   Find the value of n in the figure.
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B   The Pythagorean Theorem is true only for right triangles that have the length of the sides as whole numbers. State whether the statement is true or false.
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B   What are the side measures of the blue colored right triangle enclosed in the dot paper, if the distance between each dot is one unit?
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B   Figure ABCD is a rectangular field 136 ft long and 102 ft wide. By how much is the path from A to C shorter than the path from A to B to C?   B View Solution
B   Use Pythagorean theorem to find the length of RT¯.
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B   The length of the chord AB = 14 in. Find the radius of the circle O.
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B   Chris walked diagonally across a square garden with each side measuring 25 ft long (from one corner to the opposite corner). How far did he walk?
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B   The hypotenuse of a right triangle is 2 feet more than its longer leg. The length of shorter leg is 6 feet. Find the length of the longer leg and hypotenuse.
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B   One end of a 10 feet long wire is tied to the top of a pole and the other end is fixed on to the ground at a distance of 6 feet from the foot of the pole. What is the height of the pole?   B View Solution
B   Shethal went to a level field to fly a kite. She let out all 85 ft of string and tied it to a stake. Then she walked out on the field until she was directly under the kite, 51 ft from the stake. How high was the kite?   B View Solution
B   One side of a right triangle is 12 in and the length of its hypotenuse is 20 in. Find the length of the other side.
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B   If a = 10.2 units and b = 13.6 units, then find the measure of the hypotenuse in the right triangle.   B View Solution
B   A Pythagorean triplet when multiplied by a positive integer n is also a Pythagorean triplet. State whether the statement is true or false.   B View Solution
B   A ladder which is 15 ft long is placed on a wall such that the top of the ladder touches the top of the wall. The bottom of the ladder is 9 ft away from the wall. What is the height of the wall?
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B   What is the length of the side PR of ΔPQR in the graph, if the area of each square is 1 unit2?
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B   What are the measures of the sides of right triangle AED in the figure, if the distance between each dot in the figure is one unit?
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B   One leg of a right triangle is 18 inches long. The other leg is 4 inches less than the hypotenuse. What are the lengths of this leg and hypotenuse?
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B   The radius of the circle is 4 in. Find the length of the sides of the square.
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B   The perimeter of a right triangle is 150 inches and the ratio of the lengths of the 2 legs is 5 : 12. Find the length of the hypotenuse.
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B   The lengths of hypotenuse and shorter leg of a right triangle are in the ratio 5 : 3 and the perimeter of the triangle 96 inches. Find the length of the longer leg.
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B   Diameter of the circle O is 18 cm. Find the length of the chord AC.
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B   One leg of a right triangle is 3 in. less than the other leg. The length of the hypotenuse is 15 in. Find the lengths of the legs.
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B   The radius of the circle is 13 cm. The perpendicular distance from the center of the circle to the chord is 7.8 cm. Find the length of the chord PQ.
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B   What is the length of the third side of the triangle in the figure?   B View Solution
B   If a = 27.2 units and c = 57.8 units, then find the value of b in the figure.   B View Solution
B   If b = 16.8 units and c = 21 units, then find the value of a in the figure.   B View Solution
B   If b = 12 cm and c = 4 cm, then find the value of x in the right triangle.
   B
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B   Find the value of x in the figure. [Given b = 5.7 units, and a = 0.95 units.]   B View Solution
B   Find all the side measures of the right triangle. [Given a = 8x, b = 12x - 4 and c = 12x + 4.]   B View Solution
B   Find the length of AC¯ in the dot paper, if the distance between each dot is one unit.
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B   Find the length of the altitude BC¯ of triangle ABC if x = 17 and y = 8.
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B   What is the length of the third side of the triangle shown in the figure?[Given a = 6.6 in. and b = 8.8 in. .]   B View Solution
B   Which of the following problems can be solved using Pythagorean Theorem?
I. Nathan traveled 8 km east from home and then 6 km north. How far is he from home?
II. The diagonal of a square is 8 cm long. Find the length of the sides of the square.
III. Find the length of the third side of the triangle, if the length of the other two sides are 5 cm and 8 cm.   B
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B   P is a point in the interior of the rectangle ABCD. AP = 21 units, CP = 12 units and DP = 14 units. What is the value of BP¯?   B View Solution
B   What are the values of x and y in the triangle, if the distance between two consecutive dots is 1 unit?
   B
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B   Which of the following is true for the right triangle?   B View Solution
B   The perimeter of a right triangle is 12 units. The sum of the squares of all the sides is 50 sq.units. What is the area of the triangle?   B View Solution
B   What is the diameter of the circle with center O, if AC = 5 cm and AB = 6 cm?   B View Solution
B   The lengths p, q and r of sides of a right triangle satisfies the condition p2 - q2 = r2. What is the length of the hypotenuse?
   B
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B   The perimeter of a right triangle is 60 cm and the sum of the squares of its sides is 1250 sq.cm. Find the length of the smallest side.
   B
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