Question

the hypotenuse of a right angled triangle is 6 cm more than twice the shortest side. if the the third side is 2 cm less than the hypotenuse. find the sixe of the triangle

Answer 1

Let x = shortest side
then
2x+6 = hypotenuse
2x+6-2 = 2x+4 = long side
.
x^2 + (2x+4)^2 = (2x+6)^2
x^2 + (2x+4)(2x+4) = (2x+6)(2x+6)
x^2 + 4x^2+16x+16 = 4x^2+24x+36
5x^2+16x+16 = 4x^2+24x+36
x^2+16x+16 = 24x+36

x^2-8x+16 = 36
x^2-8x-20 = 0
(x-10)(x+2) = 0
x {-2, 10}
throw out the negative solution leaving:
x = 10m (short side)
.
hypotenuse:
2x+6 = 2(10)+6 = 20+6 = 26m
.
long side:
2x+4 = 2(10)+4 = 20+4 = 24m