(Q7)The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, Find the other two sides.

Answer:

Let the base of the right triangle = x cm

Then its altitude = x - 7 cm

By Pythagoras Theorem

x13x-7

(base)2 + (height)2 = (hypotenuse)2

x2 + (x-7)2 = 132

x2 + x2 - 14x + 49 = 169

2x2 - 14x + 49 - 169 = 0

2x2 - 14x - 120 = 0

x2 - 7x - 60 = 0

x2 - x + 5x - 60 = 0

x(x - ) + 5(x - ) = 0

(x - )(x + 5) = 0

x - = 0 (or) x + 5 = 0

x = (or) x = -5 But x cant be negative.

∴x =

x - 7 = - 7 =

The two sides are cm and cm.