Question

The corresponding sides of two similar triangles are in the ratio 3:4, then the ratios of the area of triangles is​

Answer 1

Answer:

The ratio of the area of the triangles is 9:16.

Step-by-step explanation:

Given that,

The corresponding sides of two similar triangles are in the ratio 3:4 and we are required to find the ratio of their areas.

Property of similar triangles.

If ΔABC and ΔPQR are two similar triangles then the ratios of their corresponding sides are equal i.e,

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=k$ and the ratio of areas of the triangle is

$\frac{ar(\triangle ABC)}{ar(\triangle PQR)} =(\frac{AB}{PQ})^2=(\frac{BC}{QR})^2=(\frac{AC}{PR})^2=k^2$

In the question,$k=\frac{3}{4}$

Hence, The ratio of the area of the triangle is

$\frac{ar(\triangle ABC)}{ar(\triangle PQR)} =k^2=(\frac{3}{4})^2=\frac{9}{16}$

Therefore,

The ratio of the area of the triangles is 9:16.

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Answer 2

Answer:

9/16

Step-by-step explanation:

This the correct answer

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