Question

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 $c{m}^2$. The area of the triangle is

(a) 49 $c{m}^2$ (b) $\frac{49\sqrt{3}}{4}c{m}^2$ (c) $\frac{7\sqrt{3}}{4}c{m}^2$ (d) 77 $c{m}^2$

Answer 1

Let r be the radius of the circle.

Now, the area of circle = 154 $c{m}^2$

$\pi r^2=154\frac{22}{7}\times r^2=154r^2=49r=7$

So, radius of the circle = r = 7 cm

N ow, length of each side of equilateral $△$ = a = radius of circle = 7 cm

Now, area of equilateral $△=\frac{\sqrt{3}{a}^2}{4}=\frac{\sqrt{3}(7{)}^2}{4}=12.25\times 1.732=21.217c{m}^2$