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Question

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

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Solution

Let the base be x cm. Then the altitude will be x7 cm.

By Pythagoras theroem,

x2+(x7)2=132
x2+x214x+49=169
2x214x120=0
x27x60=0
x212x+5x60=0
x(x12)+5(x12)=0
(x+5)(x12)=0
x=12,5

Length cannot be negative, then the base is 12 cm and the height is 5 cm

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