Question

The sum of two sides of a right-angled triangle containing right angle is 17 cm and its hypotenuse is 13 cm. The area of triangle is ______.

Options

• 24 cm²

• 30 cm²

• 36 cm²

• 40 cm²

Answer 1

The sum of two sides of a right-angled triangle containing right angle is 17 cm and its hypotenuse is 13 cm. The area of triangle is 30 cm².

Explanation:

Let the two legs be x and y.

Then x + y = 17 and the hypotenuse gives x² + y² = 13² = 169.

Compute (x + y)² = x² + y² + 2xy

= 17²

= 289

So, 289 = 169 + 2xy

⇒ 2xy = 120

⇒ xy = 60

Area = `1/2` × (product of the legs)

= `1/2 xx 60`

= 30 cm²