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][tex](\frac{5}{6}) ^2[/tex] = \frac{m}{108}[/tex]
⇒[tex]\frac{(5)^2}{(6)^2} = \frac{m}{108}[/tex]
or, [tex]\frac{25}{36} = \frac{m}{108} \implies m = \frac{108 \times 25}{36} = 75[/tex]
⇒ m = 75
Hence, the area of the smaller triangle is 75.
