Question

The base of a triangle is equal to the perimeter of a square whose diagonal is $9\sqrt{2}$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:

• A. 216
• B. 288
• C. 72
• D. 144

Answer 1

Answer:

A. 216

Given:

Diagonal of a square = 9√2 cm

Area of a square = 144 cm²

Formula used:

Area of a triangle = 1/2 × base × height

Perimeter of a square = 4a

Area of a square = a²

Here, a = side of a square

Calculation:

We know that diagonal of a square = a√2 

a√2 = 9√2

⇒ a = 9

Perimeter of the square = 4 × 9 = 36 cm = base of the triangle

Area of the square = 144 cm²

⇒ a² = 144 cm²

⇒ a = 12 cm = height of the triangle 

Area of the triangle = 1/2 × 36 × 12

⇒ 18 × 12 = 216

∴ Area of the triangle is 216