Question

The hypotenuse of a right angled triangle is 25 cm and its perimeter 56 cm. Find the length of the smallest side

Answer 1

Perimeter of a right angle triangle = 56cm

Sum of the two sides + hypotenuse = 56

Sum of the two sides = 56 – 25

= 31 cm

Let one side of the triangle be “x”

The other side of the triangle = (31 – x)cm

By Pythagoras theorem

AB² + BC² = AC²

x² + (31 – x)² = 25²

x² + 961 + x² – 62x = 625

2x² – 62x + 961 – 625 = 0

2x² – 62x + 336 = 0

⇒ x² – 31x + 168 = 0

(x – 24) (x – 7) = 0

x – 24 = 0 (or) x – 7 = 0

x = 24 (or) x = 7

Length of the smallest side is 7 cm