The height of a triangle is equal to the perimeter of a square whose diagonal is $$8\sqrt 2 $$ 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)

Solution(By Examveda Team)

Height of triangle = perimeter of square
Diagonal of square = $$8\sqrt 2 $$ m
∴ Length of each side of square :
$$ = \frac{{8\sqrt 2 }}{{\sqrt 2 }} = 8\,m$$
∴ 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 :
$$\eqalign{ & = \frac{1}{2} \times {\text{Base}} \times {\text{Height}} \cr & = \frac{1}{2} \times 27 \times 32 \cr & = 432{\text{ sq}}{\text{.metre}} \cr} $$