Question

the perimeters of two similar triangles are 26cm and 39 cm. find the ratio of their areas​

Answer 1

see the attachment

hope this will help you

Answer 2

Given:

Two similar triangles.

Perimeter of first triangle = 26cm.

Perimeter of second triangle = 39cm.

To find:

Ratio of areas of the given triangles.

Solution:

Let the first triangle be ABC and the second triangle be PQR. Let area and perimeter of ABC be $A_{1}$ and $P_{1}$ respectively. Let area and perimeter of PQR be $A_{2}$ and $P_{2}$ respectively.

If two triangles are similar, then their corresponding sides will be proportional, i.e., their sides will be in a reduced ratio. The reduced ratio is called scale factor.

If two triangles are similar by a scale factor of $a:b$, then the ratio of the perimeters will be in a scale factor of $a:b$ and the ratio of their areas will have a scale factor of $a^{2}:b^{2}$.

$\frac{P_{1}}{P_{2}} =\frac{26}{39}$

On further simplifying,

$\frac{P_{1}}{P_{2}} =\frac{2}{3}$

The squares of this ratio of perimeters will give the ratio of areas of the triangles.

$\frac{A_{1}}{A_{2}}=\frac{P_{1}^{2}}{P_{2}^{2}}$

$\frac{A_{1}}{A_{2}} =\frac{2^{2}}{3^{2}}$

$\frac{A_{1}}{A_{2}}=\frac{4}{9}$

Ratio of their areas is $4:9$

Ratio of areas of two similar triangles whose perimeters are given as 26cm and 39cm is 4:9.