Question

A square and an equilateral triangle have equal perimeter. If the diagonal of the square is$12\sqrt{2}$ then the area of the triangle is:

Answer 1

REF.Image

$4a=3b$ [given]

Diagonal of square = $12\sqrt{2}$

area of triangle = ?

$a^2+a^2=(12\sqrt{2}{)}^2$ $[\because$ Pythagoras theroem]

$2a^2=12\times 12\times 2$

$a^2=\frac{12\times 12\times 2}{2}$

$a=12$

$\therefore b=\frac{4}{3}\times 12=16$

$\therefore$ area = $\frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow \frac{\sqrt{3}}{4}\times 16\times 16$

$\Rightarrow 64\sqrt{3}$