Question

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

Answer 1

Suppose the sides containing right angle be x and (x – 14) cm

Area of right angled triangle 

= \(\frac { 1 }{ 2 }\) x base x altitude

= \(\frac { 1 }{ 2 }\) × x (x – 14) cm²

area = 120 cm²

⇒ 120 = \(\frac { 1 }{ 2 }\) x (x² – 14x)

⇒ x² – 14x – 240 = 0

⇒ x² – 24x + 10x – 240 = 0

⇒ x(x – 24) + 10(x – 24) = 0

⇒ (x – 24)(x + 10) = 0

either x – 24 = 0

⇒ x = 24

or x + 10 = 0

⇒ x = -10 (neglecting)

x = 24 cm (one side)

and another side = (x – 24) 

= (24 – 14) = 10 cm

Hypotenuse = √(24² + 10²) 

= √(576 + 100) 

= √676 = 26 cm

Perimeter of the triangle 

= 24 + 10 + 26 = 60 cm