Question

the hypotenus of a right angled triangle is 6 m more than twice the shorter side. if the third side is 2 m less than thehypotenus find the sides of the triangle

Answer 1

let the smallest​ side be 'x'
Hypotenuse = 2x + 6
Third side = 2x + 4
By pytahgoras theorem
(x)^2 + (2x+4)^2 = (2x+6)^2
x^2 + 4x^2 + 16 + 16x = 4x^2 + 36 + 24x
5x^2 + 16x + 16 = 4x^2 + 24x + 36
5x^2 - 4x^2 +16x - 24x + 16 - 36 = 0
x^2 - 8x -20 = 0
x^2 - 10x + 2x - 20 = 0
x( x - 10 ) + 2(x - 10) = 0
(x+10)(x+2) = 0
x = 10
x = -2
length can't be negative so x = 10
So the sides are
10m
2(10) + 6 = 26m
2(10) + 4 = 24m