Question

The hypotenuse of a right-angled triangle is 20 metres. If the difference between the lengths of the other sides be 4 metres, find the other sides.

Answer 1

Let one of the sides be x then another side is 4 + x

Applying Pythagoras theorem

$(20{)}^2=(x{)}^2+(x+4{)}^2$
$400=x^2+x^2+8x+16$
$400=2x^2+8x+16$
$2x^2+8x-384=0$
$x^2+4x-192=0$
$x^2+16x-12x-192=0$
$x(x+16)-12(x+16)=0$
$(x-12)(x+16)=0$

x= 12 or x = -16
But length can't be negative.

So one of the sides is 12 m while the other is 16 m