Question

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

Answer 1

Answer:

The area of the smaller triangle is 75.

Step-by-step 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

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

⇒$\frac{(5)^2}{(6)^2} = \frac{m}{108}$

or, $\frac{25}{36} = \frac{m}{108} \implies m = \frac{108 \times 25}{36} = 75$

⇒ m = 75

Hence, the area of the smaller triangle is 75.