- -
Solved Examples
Click on a 'View Solution' below for other questions:
fff Use Pythagorean theorem to find the length of BC¯.
 fff
View Solution
fff Use Pythagorean theorem to find the length of RQ¯.
 fff
View Solution
fff Use Pythagorean theorem to find the length of AC¯.
 fff
View Solution
fff Use Pythagorean theorem to find the length of BC¯.
 fff
View Solution
fff If a = 4.5 units and b = 6 units, then find the measure of the hypotenuse in the right triangle. fff View Solution
fff 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? fff View Solution
fff The length of the chord AB = 12 in. Find the radius of the circle O.
 fff
View Solution
fff If a = 25.6 units and c = 54.4 units, then find the value of b in the figure. fff View Solution
fff If b = 20.4 units and c = 25.5 units, then find the value of a in the figure. fff View Solution
fff If b = 27 cm and c = 9 cm, then find the value of x in the right triangle.
 fff
View Solution
fff Find the value of x in the figure. [Given b = 5.1 units, and a = 0.85 units.] fff View Solution
fff 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.
 fff
View Solution
fff Find all the side measures of the right triangle. [Given a = 6x, b = 9x - 3 and c = 9x + 3.] fff View Solution
fff What is the diameter of the circle with center O, if AC = 4 in and AB = 5 in? fff View Solution
fff 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?
 fff
View Solution
fff Find the length of the altitude BC¯ of triangle ABC if x = 5 and y = 3.
 fff
View Solution
fff 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? fff View Solution
fff 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¯? fff View Solution
fff 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?
 fff
View Solution
fff The radius of the circle is 6 in. Find the length of the sides of the square.
 fff
View Solution
fff 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.
 fff
View Solution
fff 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.
 fff
View Solution
fff Diameter of the circle O is 14 cm. Find the length of the chord AC.
 fff
View Solution
fff 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.
 fff
View Solution
fff 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?
 fff
View Solution
fff 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.
 fff
View Solution
fff 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 .] fff View Solution
fff 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? fff View Solution
fff 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.
 fff
View Solution
fff 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? fff View Solution
fff 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?
 fff
View Solution
fff If a = 6.6 units and b = 8.8 units, then find the measure of the hypotenuse in the right triangle. fff View Solution
fff The radius of the circle is 5 in. Find the length of the sides of the square.
 fff
View Solution
fff Diameter of the circle O is 22 cm. Find the length of the chord AC.
 fff
View Solution
fff 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?
 fff
View Solution
fff 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? fff View Solution
fff Use Pythagorean theorem to find the length of RT¯.
 fff
View Solution
fff Find the value of n in the figure.
 fff
View Solution
fff 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.
 fff
View Solution
fff 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?
 fff
View Solution
fff 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? fff View Solution
fff 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.
 fff
View Solution
fff Use Pythagorean theorem to find the length of RT¯.
 fff
View Solution
fff 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? fff View Solution
fff The length of the chord AB = 14 in. Find the radius of the circle O.
 fff
View Solution
fff 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?
 fff
View Solution
fff 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? fff View Solution
fff A Pythagorean triplet when multiplied by a positive integer n is also a Pythagorean triplet. State whether the statement is true or false. fff View Solution
fff 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.
 fff
View Solution
fff What is the length of the side PR of ΔPQR in the graph, if the area of each square is 1 unit2?
 fff
View Solution
fff Find the length of the altitude BC¯ of triangle ABC if x = 17 and y = 8.
 fff
View Solution
fff If a = 10.2 units and b = 13.6 units, then find the measure of the hypotenuse in the right triangle. fff View Solution
fff 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?
 fff
View Solution
fff 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?
 fff
View Solution
fff 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?
 fff
View Solution
fff The radius of the circle is 4 in. Find the length of the sides of the square.
 fff
View Solution
fff 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.
 fff
View Solution
fff 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¯? fff View Solution
fff 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.
 fff
View Solution
fff 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? fff View Solution
fff Diameter of the circle O is 18 cm. Find the length of the chord AC.
 fff
View Solution
fff 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.
 fff
View Solution
fff 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.
 fff
View Solution
fff What is the length of the third side of the triangle in the figure? fff View Solution
fff If a = 27.2 units and c = 57.8 units, then find the value of b in the figure. fff View Solution
fff If b = 16.8 units and c = 21 units, then find the value of a in the figure. fff View Solution
fff If b = 12 cm and c = 4 cm, then find the value of x in the right triangle.
 fff
View Solution
fff Find the value of x in the figure. [Given b = 5.7 units, and a = 0.95 units.] fff View Solution
fff Find all the side measures of the right triangle. [Given a = 8x, b = 12x - 4 and c = 12x + 4.] fff View Solution
fff Find the length of AC¯ in the dot paper, if the distance between each dot is one unit.
 fff
View Solution
fff 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. .] fff View Solution
fff 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. fff
View Solution
fff What are the values of x and y in the triangle, if the distance between two consecutive dots is 1 unit?
 fff
View Solution
fff Which of the following is true for the right triangle? fff View Solution
fff What is the diameter of the circle with center O, if AC = 5 cm and AB = 6 cm? fff View Solution
fff 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?
 fff
View Solution
fff 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.
 fff
View Solution