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Solved Examples
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ee  ABC, ADE are similar triangles in the figure. AD = 12 in., DB = EC = 6 in. What are the measures of AE and AC?
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ee  D and E are the mid-points of AB and AC respectively, in ΔABC. If BC = 8 cm, then what is the measure of DE?
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ee  The hexagon ABCDEF and the hexagon GHIJKL are similar and their perimeters are in the ratio of 5 : 2. If the perimeter of the hexagon GHIJKL is 10 inches, then what would be the perimeter of the hexagon ABCDEF?  ee View Solution
ee  ΔABC is similar to ΔDEF. What is mE, if mB is 39o?
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ee  Henry was playing with a torchlight and he projected a rectangular object of length 4 inches and width 3 inches on a screen. If the length of the object on the screen is 24 inches, then find the width of the object on the screen.
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ee  ΔABC is similar to ΔDEF and ABDE= BCEF = ACDF = 52. If the perimeter of the ΔABC is 25 cm, then find the perimeter of the ΔDEF.
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ee  An object seen through a telescope is in the form of a right triangle. If the actual height and base of the object is 31 and 34 ft respectively, and the height is 4 ft through the telescope, then find the length of the base of the triangle.
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ee  Paul has two similar rectangular boxes. The length and width of the smaller rectangular box are 8 inches and 6 inches respectively. If the length of the larger rectangular box is 20 inches, then what would be its width?  ee View Solution
ee  A model of a football cup was placed in a stadium. The width of the base and the height of the original cup are 120 cm and 600 cm. If the height of the model is 9 feet, then what is the width of the base of the model?
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ee  Sam saw a house and built a model similar to the house. The height and width of the model are in the ratio of 3 : 5. If the width of the model is 10 feet, then what is the height of the model?  ee View Solution
ee  The quadrilateral ABCD is similar to the quadrilateral EFGH. Find the value of n.  ee View Solution
ee  The figure shows a pair of similar hexagons. Find the value of m.
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ee  ABC, ADE are similar triangles in the figure. AD = 8 in., DB = EC = 4 in. What are the measures of AE and AC?
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ee  D and E are the mid-points of AB and AC respectively, in ΔABC. If BC = 6 ft, then what is the measure of DE?
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ee  The hexagon ABCDEF and the hexagon GHIJKL are similar and their perimeters are in the ratio of 11 : 5. If the perimeter of the hexagon GHIJKL is 25 inches, then what would be the perimeter of the hexagon ABCDEF?  ee View Solution
ee  ΔABC is similar to ΔDEF. What is mE, if mB is 68o?
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ee  The figure shows a pair of similar polygons. Find AB.  ee View Solution
ee  Sunny was playing with a torchlight and he projected a rectangular object of length 5 inches and width 4 inches on a screen. If the length of the object on the screen is 20 inches, then find the width of the object on the screen.
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ee  ΔABC is similar to ΔDEF and ABDE= BCEF = ACDF = 73. If the perimeter of the ΔABC is 35 cm, then find the perimeter of the ΔDEF.
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ee  An object seen through a telescope is in the form of a right triangle. If the actual height and base of the object is 40 and 47 ft respectively, and the height is 1 ft through the telescope, then find the length of the base of the triangle.
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ee  Bond started a journey from a point and traveled 10 miles towards south, then traveled 15 miles towards east and returned to the starting point. Pollock also started from the same point but traveled only half the distance that Bond traveled southwards, then traveled y miles towards east and returned to the starting point. Find y.  ee View Solution
ee  A rectangular poster that is 2 m long and 1.5 m wide is in the same shape as one that is 1 m long and x m wide. Find the value of x.
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ee  Is ΔABC similar to ΔEBD?
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ee  Andy has two similar rectangular boxes. The length and width of the smaller rectangular box are 8 inches and 6 inches respectively. If the length of the larger rectangular box is 20 inches, then what would be its width?  ee View Solution
ee  A model of a football cup was placed in a stadium. The width of the base and the height of the original cup are 120 cm and 600 cm. If the height of the model is 4 feet, then what is the width of the base of the model?
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ee  Find the value of x, if the figures are similar.
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ee  Are the two triangles in the figure similar?  ee View Solution
ee  Rectangle PQRS is similar to rectangle ABCD. Find the value of m.  ee View Solution
ee  Rectangles ABCD and PQRS are similar. Find the length of PR.
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ee  Are the two triangles in the figure similar, if AB is parallel to CD?  ee View Solution
ee  Are the two squares similar?
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ee  The area of a square is 32 m2. Find the area of a similar square whose dimensions are quadrupled.
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ee  Linda plays in a square-shaped ground beside their house, which has a side length of 24 m. She asks her dad to make a similar playing area in their house, whose area is 116 of the area of the ground. What must be the side length of the new ground?  ee View Solution
ee  The measure of each angle of a regular hexagon is 120°. A similar hexagon is formed by tripling the dimensions of the original hexagon. What will be the measure of each angle of the new hexagon?
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ee  A regular octagon measures 10 cm on each side. A similar octagon is formed by halving the side length of the original octagon. What will happen to the perimeter of the new octagon?  ee View Solution
ee  The ratio of the areas of two regular hexagons is 1 : 36. Find the perimeter of the smaller hexagon, if the side length of the bigger hexagon is 12 cm.  ee View Solution
ee  The radii of two similar spheres are 12 cm and 18 cm. Find the ratio of their volumes.
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ee  Frank wants to make an advertisement board similar to another advertisement board, which has a length and width of 21 feet and 14 feet. He wants to have a length of 15 feet for the new board. What will be the width of the board that he wants to make?  ee View Solution
ee  A regular hexagon measures 9 cm on each side. A similar hexagon is formed by halving the side length of the original one. What will happen to perimeter of the new hexagon?  ee View Solution
ee  The side length of a heptagon is given as 10 in. A similar heptagon is formed by multiplying the side length of the original one by 3. What will happen to perimeter of the new heptagon?
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ee  A regular pentagon measures 4 cm on each side. A similar pentagon is formed by doubling the side length of the original one. What will happen to the perimeter of the new pentagon?  ee View Solution
ee  Sid plans to expand the existing square flowerbed by quadrupling its dimensions. What sort of change does this expansion bring in the area of the square flowerbed?  ee View Solution
ee  Kay put a 6 by 4 cm picture on a photocopier and doubled its length and halved its width. What will happen to the area of the picture?  ee View Solution
ee  Paul used a rubber band in a geoboard to make a triangle of area 72 cm2. What happens to the area of the triangle, if he doubles the base and keeps the height constant?  ee View Solution