Question

The hypotenuse of a right angled triangle is25 cm and its perimeter 56 cm.Find the length of the smallest side
​

Answer 1

Suppose that the lengths of the sides making the right angle are x and y.

Since, it is a right angled triangle and hypotenuse is 25, we have,

x² + y² = (25)²....................(1).

Further, the perimeter is 56 cm, so we get,

x + y + 25 = 56    or,

x + y = 31 .................(2).

y = 31 − x .................(3)

Substituting value if y in (1) ;

x² + (31 − x)² = 625.

x² + ( (31)² − 62x + x²) − 625=0.

2x² + 961 - 62x - 625 = 0.

2x² - 62x + 336 = 0

x² - 31x + 168 = 0

x² - 24x - 7x + 168 = 0

x (x - 24) - 7 (x - 24) = 0

(x - 7) (x - 24) = 0

x = 7  or x = 24

Putting value of x in (3) equation ;

If x = 7 ,

y = 31 - 7 = 24

If x = 24 ,

y = 31 - 24 = 7

Hence, in either case length of smaller side will be 7 whether it is x or y.