Question

Area of two similar triangles are in the ratio 9:16. Sides of the triangles are in the ratio will be what?

Answer 1

LET THE TWO SIMILAR TRIANGLES BE TRIANGLE ABC AND PQR .
so,

$\frac{ar(abc)}{ar(pqr)} = \frac{ {(ab)}^{2} }{ {(pq)}^{2} } = \frac{9}{16}$
$so \\ \frac{ab}{pq} = \: \frac{ \sqrt{9} }{ \sqrt{16} } = \frac{3}{4}$
therefore the ans is
$\frac{3}{4}$

Answer 2

Sides of the triangles are in the ratio 3:4

Step-by-step explanation:

Theorem : The ratio of the square of the corresponding sides of two similar triangles is equal to the ratio of area of similar triangles

We are given that Area of two similar triangles are in the ratio 9:16.

So, By theorem :

$\frac{9}{16}=(\frac{\text{Side of triangle 1}}{\text{Side of triangle 2}})^2\\\\\sqrt{\frac{9}{16}}=(\frac{\text{Side of triangle 1}}{\text{Side of triangle 2}})\\\\\frac{3}{4}=\frac{\text{Side of triangle 1}}{\text{Side of triangle 2}}$

Hence Sides of the triangles are in the ratio 3:4

#Learn more:

The areas of two similar triangles are 36cm and 64cm. If one side of the former triangle is 6cm then the corresponding side of the later triangle will be​

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