The base of a triangle is equal to the perimeter of a square whose diagonal is 6√2 cm, and its height is equal to the side of a square whose area is 144 cm2. The area of the triangle (in cm2) is :
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 144.
We know that,
Diagonal of square = √2a
Area of triangle = 1/2 × base × height and,
Perimeter of square = 4 × side
Now,
⇒ √2a = 6√2
So, a(side) = 6
Base = 6 × 4 = 24
Now, the height is equal to the side of the square whose area is 144 cm2
⇒ b2 = 144
⇒ b = 12
Now,
Height = Side of square
So,
Area of triangle = 1/2 × 12 × 24 = 144 cm2