Question

a square and an equilateral traiangle have equal perimeters . if the diagonal of square is 12√2 cm find the area of triangle

Answer 1

$\text{Side of Square}=\frac{\text{Diagonal}}{\sqrt{2}}\\=\frac{12\sqrt{2}}{\sqrt{2}}\\=12 cm\\\text{Perimeter of Square}=\text{Perimeter of triangle}\\\Rightarrow 4\times \text{Side of Square}=3\times \text{Side of equilateral triangle}\\\Rightarrow 4\times 12=3\times \text{Side of equilateral triangle}\\\Rightarrow \text{Side of equilateral triangle}=16 cm\\\text{Area of Equilateral}=\frac{\sqrt{3}}{4}{\text{Side}}^{2}\\= \frac{\sqrt{3}}{4}{16}^{2}\\=64\sqrt{3} {cm}^{2}$