Question

A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.

Answer 1

Perimeter of a right angled triangle = 112 cm
Hypotenuse = 50 cm
∴ Sum of other two sides = 112 – 50 = 62 cm
Let the length of first side = x
and length of other side = 62 – x
According to the condition
(x)² + (62 – x)² = (50)²  ...(By Pythagorus Theorem)
⇒ x² + 3844 – 124x + x² = 2500
⇒ 2x² – 124x + 3844 – 2500 = 0
⇒ 2x² – 124 + 1344 = 0
⇒ x² – 62x + 672 = 0   ...(Dividing by 2)
⇒ x² – 48x – 14x + 672 = 0
⇒ x(x –  48) –14(x - 48) = 0
⇒ (x – 48)(x – 14) = 0
Either x – 48 = 0,
then x = 48
or
x – 14 = 0,
then x = 14
(i) If x = 48,
then one side = 48cm
and other side = 62 – 48 = 14cm
(ii) If x = 14,
then one side = 14cm
and other side = 62 – 14 = 48
Hence sides are 14cm, 48cm.