Question

If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.

Answer 1

Answer:

16

:

81

Explanation:

Scale factor for the sides of these triangles.

k

=

4

9

.

Therefore the ratio of area will be:

k

2

=

Area Triangle A

Area triangle B

k

2

=

(

4

9

)

2

=

16

81

Answer 2

Ratio of areas of similar triangles is 9 : 25.

Solution:

Given data:

Ratio of sides of two similar triangles = 3 : 5

To find the ratio of areas of the triangles:

We know that,

In two triangles are similar, then the ratio of their area is equal to the square of the ratio of their sides.

$\text{Ratio of areas} = \frac{\text{Area of triangle 1}}{\text{Area of triangle 2} }$

                      $=\left(\frac{3}{5}\right) ^2$

                      $=\frac{9}{25}$

Ratio of areas of similar triangles is 9 : 25.