The hypotenuse of a right triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.
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Let the length of the shortest side =x
Hypotenuse =2x+6
Third side =2x+6-2=2x+4
Hypotenuse square = sum of the squares of other two sides
(2x+6)^2 = x^2+(2x+4)^2
4x^2+24x+36=x^2+4x^2+16x+16
0=5x^2-4x^2+16x+16-24x-36
0= x^2-8x-20
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=0 or x+2=0
x =10 or x=-2
x should not be negative
x=10
Shortest side =x=10
Hypotenuse =2x+6=2*10+6=26
Third side =2x+4=2*10+4=24
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