The height of a triangle is equal to the perimeter of a square whose diagonal is 8 2 metre and the base of the same triangle is equal to the side of a square whose area is 729 sq.metre. What is the area of the triangle ? (in sq. metre)

Answer: Option D

Height of triangle = perimeter of square
Diagonal of square = $$8\sqrt{2}$$ m
∴ Length of each side of square :
$$=\frac{8\sqrt{2}}{\sqrt{2}}=8m$$
∴ Perimeter of square = 4 × 8 = 32 m = Height
Area of other square = 729
Side of square = $$\sqrt{729}$$  = 27 m = base of triangle
∴ Area of triangle :
$$\begin{array}{rl}& =\frac{1}{2}\times \text{Base}\times \text{Height}\\ & =\frac{1}{2}\times 27\times 32\\ & =432\text{ sq}\text{.metre}\end{array}$$