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# Similar Figure and Pythagorean Theorem Word Problems Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Similar Figure and Pythagorean Theorem Word Problems Study Guide.

## Similar Figure and Pythagorean Theorem Word Problems Practice Questions

### Practice 1

#### Problems

1. A triangle has sides 4 m, 5 m, and 6 m. What is the measure of the longest side of a similar triangle whose shortest side is 16 m?
2. A triangle has sides 7 in., 10 in., and 11 in. What is the measure of the shortest side of a similar triangle whose longest side is 33 in.?
3. One rectangle has sides that are four times the size of another rectangle. If the measures of the sides of the larger rectangle are 24 cm and 32 cm, respectively, what are the measures of the sides of the smaller rectangle?
4. Two quadrilaterals are similar, and the measures of the sides of one figure are 2 m, 4 m, 5 m, and 8 m, respectively. What is the measure of the longest side of the other quadrilateral if the measure of the shortest side is 12 m?

#### Solutions

1. Read and understand the question. This question is looking for the value of the longest side in a figure with two similar triangles.
2. Make a plan. Use the strategy of drawing a picture. Then, line up the corresponding sides in a proportion. Finally, cross multiply to find the value of x, the unknown side.

Carry out the plan. First, draw a picture. The picture of the two triangles follows.

Next, identify the corresponding sides. The side labeled 6 m corresponds with the side labeled x, and the side labeled 4 m corresponds with the side labeled 16 m. Set up a proportion using the corresponding parts. Use the proportion

The proportion is

Cross multiply to get 4x = 96. Divide each side of the equation by 4 to get x = 24. The value of x is 24 m.

Check your answer. To check this solution, substitute x = 24 into the proportion and cross multiply to be sure that the cross products are equal. The proportion becomes

Cross multiply to get 96 = 96. The cross products are equal, so this answer is checking.

3. Read and understand the question. This question is looking for the value of the shortest side in a figure with two similar triangles.
4. Make a plan. Use the strategy of drawing a picture. Then, line up the corresponding sides in a proportion. Finally, cross multiply to find the value of x, the unknown side.

Carry out the plan. First, draw a picture. The picture of the two triangles appears next.

Next, identify the corresponding sides. The side labeled 7 corresponds with the side labeled x, and the side labeled 11 corresponds with the side labeled 33. Set up a proportion using the corresponding parts. Use the proportion

The proportion is

Cross multiply to get 11x = 231. Divide each side of the equation by 11 to get x = 21. The value of x is 21 m.

Check your answer. To check this solution, substitute x = 21 into the proportion and cross multiply to be sure that the cross products are equal. The proportion becomes

Cross multiply to get 231 = 231. The cross products are equal, so this answer is checking.

5. Read and understand the question. This question is looking for the lengths of the sides of a rectangle when the sides of a similar rectangle are given.
6. Make a plan. The sides of similar figures are in proportion. In this question, the sides of the larger rectangle are 4 times as large as the sides of a smaller rectangle. Divide the measures of these sides by 4 to find the lengths of the sides of the smaller rectangle.

Carry out the plan. The sides of the larger rectangle are 24 and 32. Twenty four divided by 4 is 6 and 32 divided by 4 is 8. The sides of the smaller rectangle are 6 cm and 8 cm.

Check your answer. To check this solution, multiply the sides of the smaller rectangle by 4.

6 × 4 = 24

and

8 × 4 = 32

so this solution is checking.

7. Read and understand the question. This question is looking for the missing side of a quadrilateral.
8. Make a plan. Use the strategy of drawing a picture. Then, line up the corresponding sides in a proportion. Finally, cross multiply to find the value of x, the missing side.

Carry out the plan. First, draw a picture. The picture of the two quadrilaterals appears next.

Next, identify the corresponding sides. The side that is 2 m corresponds with the side that is 12 m, and the side that is 8 m corresponds with the unknown side, or x. Set up a proportion using the corresponding parts. Use the proportion

The proportion is

Cross multiply to get 2x = 96. Divide each side of the equation by 2 to get x = 48. The length of the longest side is 48 m.

Check your answer. To check this solution, substitute x = 48 into the proportion and cross multiply to be sure that the cross products are equal. The proportion becomes

Cross multiply to get 96 = 96. The cross products are equal, so this solution is checking.

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