Question

The perimeter of a right-angled triangle is 60 cm. Its hypotenuse is 26 cm. Find the area of the triangle.

Answer 1

Let base and height of a right angled triangle be b and h cm respectively

b + h + 26 = 60

⇒ b + h = 34

⇒ (b + h)² = (34)²

Also b² + h² = (26)² …(ii)

Subtracting (ii) from (i), we get

(b + h)² – (b² + h²) = (34)² – (26)²

⇒ b² + h² + 2bh – b² – h² = (34 – 26)(34 + 26)

⇒ 2bh = 8 x 60

⇒ bh = 240

⇒ Area = \(\frac { 1 }{ 2 }\) x b x h 

= \(\frac { 1 }{ 2 }\) x 240 = 120

Hence, area =120 cm²