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

Let base of the right triangle is x cm. Then the altitude is x-7 cm.

Then by the property of right triangle and using the given property we have

x²+(x-7)² = (13)²

x²+ x²-14x+49 = 169

2x²-14x-120 = 0

x²-7x-60 = 0

x²-12x+5x-60 = 0

x(x-12)+5(x-12) = 0

(x-12)(x+5) = 0

x-12 = 0

x =12

or, x+5 = 0

x = -5

Since length can’t be negative, so x = -5 is not possible.

Hence the base is 12 cm and the altitude is (12-7)cm = 5 cm