Question

The difference between the sides at a right angle in a right-angled triangle is 14 cm. The area of the triangle is 120 cm², The perimeter of the triangle is -

1. 68 cm
2. 64 cm
3. 60 cm
4. 58 cm

Answer 1

Correct Answer - Option 3 : 60 cm

Given:

The difference between the sides at a right angle in a right-angled triangle is 14 cm.

The area of the triangle is 120 cm².

Formula Used:

Perimeter = Sum of all sides

Area of right-angled triangle = 1/2 × Base × Height

Calculation:

Let the base of the triangle be x.

Then the height of the triangle = x + 14

The area of the triangle is 120 cm2.

⇒ 1/2 × x × (x + 14) = 120

⇒ x² + 14x = 240

⇒ x2 + 14x - 240 = 0

⇒ x = - 24, 10

Base of the triangle = 10 cm

Height of the triangle = 24 cm

By Pythagoras theorem,

Hypotenuse = √24² + 10² = √576 + 100 = 26 cm

Perimeter = 24 + 10 + 26 = 60 cm

∴ The perimeter of the triangle is 60 cm.