Question 1

Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm, and 5 cm. The shortest side of the second triangle is 6 cm. What is the length of the longest side of the second triangle?

Accepted Answer

$$10\ 	ext{cm}$$

Question 2

A building casts a shadow that is 45 meters long. At the same time, a 2-meter-tall sign casts a shadow that is 6 meters long. How tall is the building?

Accepted Answer

$$15\ 	ext{meters}$$

Question 3

If two triangles are similar and the ratio of their corresponding sides is $$\dfrac{5}{3}$$, what is the ratio of their perimeters?

Accepted Answer

$$\dfrac{5}{3}$$

Question 4

Jerry is 6 feet tall and his shadow measures 9 feet long. At the same time, a rock casts a shadow of 580 feet. How tall is the rock?

Accepted Answer

$$387\ 	ext{feet}$$

Question 5

Which of the following statements is TRUE about similar triangles?

Accepted Answer

Corresponding angles are equal and corresponding sides are proportional.

Question 6

A photograph measures $$4\ 	ext{inches} by$$ $$6\ 	ext{inches}. If it is $$enlarged so that the shorter side is $$10\ 	ext{inches}$$, what is the length of the longer side?

Accepted Answer

$$15\ 	ext{inches}$$

Question 7

If triangle ABC is similar to triangle DEF, and $$AB = 8$$, $$BC = 10$$, $$CA = 12$$, and $$DE = 4$$, what is the length of $$EF$$?

Accepted Answer

$$5$$

Question 8

A rectangular billboard is $$12\ 	ext{ft}$$ wide and $$9\ 	ext{ft}$$ tall. A scale model is made with a width of $$4\ 	ext{inches}. $$What is the height of the model?

Accepted Answer

$$3\ 	ext{inches}$$

Question 9

If two similar triangles have areas in the ratio $$9:16$$, what is the ratio of their corresponding sides?

Accepted Answer

$$\dfrac{3}{4}$$

Question 10

A map uses a scale of $$1\ 	ext{cm}$$ : $$5\ 	ext{km}. If $$the distance between two cities on the map is $$7\ 	ext{cm}$$, what is the actual distance between the cities?

Accepted Answer

$$35\ 	ext{km}$$

Question 11

A triangle has sides of $$5\ 	ext{cm}$$, $$7\ 	ext{cm}$$, and $$8\ 	ext{cm}. A $$similar triangle has its shortest side measuring $$10\ 	ext{cm}. $$What is the length of its longest side?

Accepted Answer

$$16\ 	ext{cm}$$

Question 12

A tree casts a shadow of $$24\ 	ext{ft} at $$the same time a $$6\ 	ext{ft}$$ pole casts a shadow of $$3\ 	ext{ft}. $$How tall is the tree?

Accepted Answer

$$48\ 	ext{ft}$$

Question 13

Which of the following is NOT a property of similar triangles?

Accepted Answer

Corresponding sides are equal in length.

Question 14

A rectangular field is $$60\ 	ext{m}$$ long and $$40\ 	ext{m}$$ wide. On a blueprint, the field is represented by a rectangle $$15\ 	ext{cm}$$ long. What is the width of the rectangle on the blueprint?

Accepted Answer

$$10\ 	ext{cm}$$

Question 15

If the ratio of the sides of two similar triangles is $$2:5$$, what is the ratio of their areas?

Accepted Answer

$$4:25$$

Question 16

A model car is built at a scale of $$1:18. If $$the actual car is $$162\ 	ext{inches}$$ long, how long is the model car?

Accepted Answer

$$9\ 	ext{inches}$$

Question 17

A triangle has sides $$a$$, $$b$$, and $$c. A $$similar triangle has sides $$ka$$, $$kb$$, and $$kc. $$What is the ratio of the areas of the two triangles?

Accepted Answer

$$k^2$$:1$$

Question 18

A mural is $$20\ 	ext{ft}$$ wide and $$8\ 	ext{ft}$$ tall. An artist wants to create a scale drawing with a width of $$5\ 	ext{inches}. $$What should be the height of the drawing?

Accepted Answer

$$2\ 	ext{inches}$$

Similarity of Triangles and Applications in Geometry

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