# 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.

**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.

**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 cm^{2}, 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 cm^{2}, calculate the area of each triangle.

- A
216 cm
^{2}, 72 cm^{2} - B
96 cm
^{2}, 192 cm^{2} - C
36 cm
^{2}, 324 cm^{2}

**Q16: **

The sum of the areas of two similar triangles is 740 cm^{2}.
Given that the ratio between their perimeters is , find the areas of both triangles.

- A
2 713 cm
^{2}, 312 cm^{2} - B
1 018 cm
^{2}, 202 cm^{2} - C
256 cm
^{2}, 484 cm^{2}

**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