FINDING MISSING MEASURES OF SIMILAR TRIANGLES WORKSHEET

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 ?

Solution

Problem 2 :

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

Solution

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

Solution

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

Solution

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.

Solution

Problem 1 :

Triangle HIJ is similar to triangle STR, what is the perimeter of triangle STR

Solution

Problem 2 :

If the two triangles are similar

Find

i) Scale factor

ii) Ratio of perimeter

iii)  Ratio of area

Solution

Problem 3 :

Two triangles have a scale factor of 2/3. The area of the larger triangle is 12 cm². What is the area of smaller triangle.

Solution

Problem 4 :

If the length of each side of triangle is cut to 1/3 of its original size, what happens to the area of the triangle ?

The new area is _______________ of the original area.

Solution

Problem 5 :

For the two triangles below to be similar, which of the following be true ?

a)  x = 2y/3    b)  c = 3y/2     c)  x = 3y     d)  x = y

Solution

Problem 6 :

An architect is building a model of a tennis court for a new client. On the model, the court is 6 inches wide and 13 inches long. An official tennis court is 36 feet wide. What is the length of a tennis court ?

Solution

Problem 7 :

Your family has decided to put a rectangular patio in your backyard, similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio.

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

Solution

Problem 9 :

What is the perimeter of the rectangle?

b) What is the area of the rectangle?

c) If the width of the rectangle is doubled, what do you think happens to the perimeter?

d) If the width of the rectangle is doubled, what do you think happens to the area?

Solution