Question

The area of two similar triangles are respectively 9cm^2 and 16cm^2 . The ratio of their corresponding sides is:

Answer 1

Answer:

Area of the triangles is in the ratio 9:16

we know that the ratio of area of two triangles is equal to the ratio of square of the corresponding sides

⇒ 9/16 = 3/4

∴ their sides would be in the ratio 3:4

Answer 2

Answer:

The ratio of the corresponding sides is 3:4

Step-by-step explanation:

Given:

The ratio of the area of two similar triangles.

$\frac{area1}{area2}=\frac{9}{16}$

To find:

The ratio of the corresponding sides of the two triangles.

Step 1:

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the sides of the triangles.

$\frac{area1}{area2}=\frac{side1^{2} }{side2^{2} }$

Step 2:

Substituting the given values, we get

$\frac{9}{16}=\frac{side1^{2} }{side2^{2} }$

Taking positive square roots on both sides.

$\frac{3}{4}=\frac{side1 }{side2 }$

Therefore, the ratio of the corresponding sides of the two similar triangles is 3:4

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