FIND MISSING SIDE OF SIMILAR FIGURES WORKSHEET

Find x given that the figures are similar :

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 6 :

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Problem 7 :

A town plans to build a new swimming pool. An Olympic pool is rectangular with a length of 50 meters and a width of 25 meters. The new pool will be similar in shape to an Olympic pool but will have a length of 40 meters. Find the perimeters of an Olympic pool and the new pool

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Problem 8 :

In the diagram, △ABC ∼ △DEF. Find the area of △DEF.

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Problem 9 :

A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.

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Problem 10 :

Describe and correct the error in finding the area of rectangle B. The rectangles are similar.

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Problem 11 :

In the following the two polygons are similar. Find the values of x and y.

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Problem 12 :

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Problem 13 :

In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.

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Find the missing length. The triangles in each pair are similar.

Problem 1 :

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Problem 2 :

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Problem 3 :

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Solve for x. The triangles in each pair are similar.

Problem 5 :

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Problem 6 :

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Problem 7 :

In the following figure, JKLM ∼ EFGH

a) Find the scale factor of JKLM to EFGH.

b) Find the scale factor of EFGH to JKLM.

c) Find the values of x, y, and z.

d)  Find the perimeter of each polygon.

e) Find the ratio of the perimeters of JKLM to EFGH.

f)  Find the area of each polygon.

g) Find the ratio of the areas of JKLM to EFGH.

Solution

Problem 8 :

Rectangle A is similar to rectangle B. Rectangle A has side lengths of 6 and 12. Rectangle B has a side length of 18. What are the possible values for the length of the other side of rectangle B? Select all that apply.

a) 6     b)  9    c)  24    d) 36

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Problem 1 :

Lance and Alien is 5 feet tall. His shadow is 8 feet long.

At the same time of day, a tree's shadow is 32 feet long. What is the height of the tree ?

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Problem 2 :

Pentagon JKLMN is similar to pentagon VWXYZ, what is the measurement of angle X ?

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Problem 3 :

Triangle PQR is similar to triangle DEF as shown.

which describes the relationship between the corresponding sides of the two triangles ?

a)  PQ/DE = 4/6        b)  PQ/DE = 6/4

c)  PQ/EF = 4/9        d)  PR/DE = 6/6

Solution

Problem 4 :

A six foot tall person is standing next to flag pole. The person is casting a shadow 1 1/2 feet in length while a flagpole is casting a shadow 5 feet in length. How tall is the flagpole ?

a)  30 ft     b) 25 ft    c)  20 ft     d)  15 ft

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Problem 5 :

The angle of the roof on Kaya's doll house is 56°. She built a scale model of the doll house with a scale ratio of 1 : 4, what is the measure of the angle of the roof of the model ?

a) 14°     b) 34°    c) 56°    d)  224°

Solution

Problem 6 :

In triangle PQR is similar to XYZ.

What is the perimeter of XYZ ?

a) 21 cm     b) 63 cm    c) 105 cm    d)  126 cm

Solution

Problem 7 :

If the triangles ADE and ABC shown in the figure below are similar, what is the value of x ?

a) 4     b) 5    c) 6    d)  8     e)  10

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Problem 8 :

In the figure given below, the two triangles are similar. What is the value of x ?

a) 12.4     b) 13.2    c) 14    d)  18.6     e)  22.1

Solution

Problem 9 :

Mr. Smith is having some photos enlarged for studio. He wants to enlarge a photo that is 5 inches by 7 inches so the dimensions are 3 times larger than the original. How many times larger than the original photo will the area of the new photo be ?

a) 3     b) 6    c) 9    d)  30

Solution

Problem 10 :

During a total eclipse of the Sun, the moon is directly in line with the Sun and blocks the Sun’s rays. The distance DA between Earth and the Sun is 93,000,000 miles, the distance DE between Earth and the moon is 240,000 miles, and the radius AB of the Sun is 432,500 miles. Use the diagram and the given measurements to estimate the radius EC of the moon.

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