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In this lesson, we will learn how to recognize and use proportional relationships of corresponding perimeters of similar triangles to solve problems.

Q1:

The ratio of the areas of two similar triangles is 9 1 0 0 . If the perimeter of the larger triangle is 129, what is the perimeter of the smaller one?

Q2:

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.

Q3:

In the diagram, β³ π· πΈ πΉ βΌ β³ πΆ π΅ πΉ and the perimeter of β³ πΆ π΅ πΉ is 104. Given that π· πΉ = 2 1 and πΉ πΆ = 2 8 , find the perimeter of β³ π· πΈ πΉ .

Q4:

In the diagram, β³ π· πΈ πΉ βΌ β³ πΆ π΅ πΉ and the perimeter of β³ πΆ π΅ πΉ is 178. Given that π· πΉ = 2 5 and πΉ πΆ = 4 0 , find the perimeter of β³ π· πΈ πΉ .

Q5:

Suppose β³ π΄ π΅ πΆ βΌ β³ π· πΈ πΉ . If the ratio of the perimeter of β³ π΄ π΅ πΆ to that of β³ π· πΈ πΉ is 2 5 , and the sum of their areas is 64 cm^{2}, determine their areas rounded to the nearest hundredth.

Q6:

Given that β³ π΄ π΅ πΆ and β³ π π π are similar triangles, π΄ π΅ π π = 5 8 , and the perimeter of β³ π΄ π΅ πΆ is 28.1 cm, find the perimeter of β³ π π π to the nearest tenth.

Q7:

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.

Q8:

The sum of the areas of two similar triangles is 740 cm^{2}. Given that the ratio between their perimeters is 8 βΆ 1 1 , find the areas of both triangles.

Q9:

The figure shows triangles π΄ π΅ πΆ and πΆ π· πΈ , where πΆ lies on π΄ π· and π΅ πΈ .

Work out the value of π₯ .

Work out the value of π¦ .

Work out the perimeter of β³ π΄ π΅ πΆ .

Q10:

π΄ π΅ πΆ and π· πΈ πΉ are similar triangles. Suppose that the ratio of the area of β³ π΄ π΅ πΆ to the area of β³ π· πΈ πΉ is 1 4 , the perimeter of β³ π΄ π΅ πΆ is 230, and πΈ πΉ = 7 6 . Determine the perimeter of β³ π· πΈ πΉ and π΅ πΆ .

Q11:

π΄ π΅ πΆ is a triangle whose side lengths are 43 cm, 39 cm, and 54 cm. If β³ π΄ π΅ πΆ βΌ β³ π π πΏ and the perimeter of β³ π π πΏ = 6 8 c m , find the side lengths of β³ π π πΏ .

Q12:

π΄ π΅ πΆ is a triangle whose side lengths are 30 cm, 39 cm, and 48 cm. If β³ π΄ π΅ πΆ βΌ β³ π π πΏ and the perimeter of β³ π π πΏ = 4 6 . 8 c m , find the side lengths of β³ π π πΏ .

Q13:

If π΄ πΈ = 1 3 . 6 c m and π· πΈ = 1 3 . 7 c m , find the perimeter of β³ πΈ π΅ πΆ .

Q14:

The ratio between the lengths of two corresponding sides of two similar polygons is 2 βΆ 9 . If the perimeter of the smaller polygon is 68 cm, determine the perimeter of the bigger one rounded to two decimal places.

Q15:

Find the perimeter of β³ π΄ π΅ πΆ .

Q16:

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

Q17:

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.

Q18:

The figure shows triangle π΄ π΅ πΆ .

Q19:

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

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