# Worksheet: Proportions in Similar Triangles

In this worksheet, we will practice recognizing and using proportional relationships of corresponding perimeters of similar triangles to solve problems.

Q1:

The ratio of the areas of two similar triangles is . If the perimeter of the larger triangle is 129, what is the perimeter of the smaller one?

Q2:

One of two similar triangles has a perimeter of 51 cm, while the side lengths of the other are 87.5 cm, 49 cm, and 42 cm. Find the length of the longest side in the first triangle.

Q3:

is a triangle whose side lengths are 43 cm, 39 cm, and 54 cm. If and the perimeter of , find the side lengths of .

• A 86 cm, 78 cm, 108 cm
• B 5.375 cm, 4.875 cm, 6.75 cm
• C 43 cm, 39 cm, 54 cm
• D 21.5 cm, 19.5 cm, 27 cm

Q4:

Given that and are similar triangles, , and the perimeter of is 28.1 cm, find the perimeter of to the nearest tenth.

Q5:

The ratio between the lengths of two corresponding sides of two similar polygons is . If the perimeter of the smaller polygon is 68 cm, determine the perimeter of the bigger one rounded to two decimal places.

Q6:

The perimeter of the one of two similar triangles is 31.5 cm, and the side lengths of the other are 9 cm, 2 cm, and 10 cm. Find the length of the longest side of the first triangle rounded to two decimal places.

Q7:

In the diagram, and the perimeter of is 104. Given that and , find the perimeter of .

Q8:

Find the perimeter of .

Q9:

Complete the following: The ratio between the two perimeters of two similar triangles is equal to the ratio between .

• Atheir areas
• Btheir angles
• Ctheir sides squared
• Dtheir corresponding sides
• Etheir sides cubed

Q10:

Suppose . If the ratio of the perimeter of to that of is , and the sum of their areas is 64 cm2, determine their areas rounded to the nearest hundredth.

• Aarea of , area of
• Barea of , area of
• Carea of , area of
• Darea of , area of
• Earea of , area of

Q11:

If and , find the perimeter of .

Q12:

Given that the triangles shown are similar, what is the perimeter of the larger one?

Q13:

The figure shows triangle .

Work out the value of .

Work out the value of .

Work out the perimeter of .

Q14:

The figure shows triangles and , where lies on and .

Work out the value of .

Work out the value of .

Work out the perimeter of .

Q15:

The ratio between the perimeters of two similar triangles is :. Given that the difference between their areas is 288 cm2, calculate the area of each triangle.

• A 216 cm2, 72 cm2
• B 96 cm2, 192 cm2
• C 36 cm2, 324 cm2

Q16:

The sum of the areas of two similar triangles is 740 cm2. Given that the ratio between their perimeters is , find the areas of both triangles.

• A 2 713 cm2, 312 cm2
• B 1 018 cm2, 202 cm2
• C 256 cm2, 484 cm2

Q17:

and are similar triangles. Suppose that the ratio of the area of to the area of is , the perimeter of is 230, and . Determine the perimeter of and .

• A perimeter of ,
• B perimeter of ,
• C perimeter of ,
• D perimeter of ,
• E perimeter of ,

Q18:

In the diagram, and the perimeter of is 178. Given that and , find the perimeter of .

Q19:

is a triangle whose side lengths are 30 cm, 39 cm, and 48 cm. If and the perimeter of , find the side lengths of .

• A 75 cm, 97.5 cm, 120 cm
• B 1.92 cm, 2.496 cm, 372 cm
• C 30 cm, 39 cm, 48 cm
• D 12 cm, 15.6 cm, 19.2 cm
• E 2.4 cm, 3.12 cm, 3.84 cm

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