Question

24. If the ratio of the perimeter of two similar triangles is 4:25, then what is the ratio of their areas​

Answer 1

Answer:

16:625

the ratio of their areas

Answer 2

Given:

✰ The ratio of the perimeter of two similar triangles is 4:25.

To find:

✠ The ratio of the areas of two similar triangles.

Solution:

Here, we will use proportional perimeter theorem.

We know that the ratio of the perimeter of two similar triangles is 4:25, so the ratio of corresponding sides of two triangles and the ratio of the perimeter of two triangles is same.

So,

➛ The ratio of the perimeter of two triangles = The ratio of corresponding sides of two triangles

➛ The ratio of corresponding sides of two triangles = 4:25

Now,

➛ The ratio of the areas of two similar triangles = The ratio of squares of corresponding sides of two triangles

➛ The ratio of the areas of two triangles = 4²/25²

➛ The ratio of the areas of two triangles = (4 × 4)/(25 × 25)

➛ The ratio of the areas of two triangles = 16/625

➛ The ratio of the areas of two triangles = 16:625

∴ The ratio of the areas of two similar triangles = 16:625

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