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

Answer 1

Let base be x cm , then altitude will be (x-7) cm.

Now ,

By using pythagoras theorem-

132 = x2 + (x-7)2

169 = x2 + x2 + 49 - 14x

2x2 - 14x - 120 = 0

x2 - 7x - 60 = 0

x2 - 12x + 5x - 60 = 0

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

Hence x = 12

sO , Altitude is 5 cm

AND. ,

base = 12cm

Answer 2

let the base of the triangle be Xm
attitude is x - 7
by P.G.T hypotenuse square =base square +perpendicular square
13square =X square +(X-7) square
169 =x square +x square -14x+49
169=2x square -14x +49
2x square -14x +49 -269
2x square -14x -120
therefore x=12
base =12
altitude =12-7
=5 cm