Question

11 The sides of two similar triangle are in a ratio of 5:6. The area of the larger triangle is 108.

Find the area of the smaller triangle. (1 point)

Answer 1

The area of the smaller triangle is 75.

Explanation:

Here, the ratio of the sides of the similar triangle are 5 : 6

The area if the larger triangle = 108

let us assume that the area of the smaller triangle = m

By the Theorem:

In two similar triangles, the ratio of the areas of similar triangles is the square of the ratio of their sides.

Similarly, here

`[tex]((5)/(6)) ^2` = \frac{m}{108}[/tex]

⇒
`((5)^2)/((6)^2)   = (m)/(108)`

or,
`(25)/(36)   = (m)/(108)  \implies m = (108 * 25)/(36)  = 75`

⇒ m = 75

Hence, the area of the smaller triangle is 75.