The hypotenuse of a right triangle is 6m more than the twice of the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.

Explanation

Let, the length of the shortest side be x metres then hypotenuse= (2x+6) metres
and the third side =(2x+6-2) metres
=(2x+4) metres
Now, using Pythagoras theorem
`(2x+6)^(2)=x^(2)+(2x+4)^(2)`
`implies(4x^(2)+24x+36)=x^(2)+(4x^(2)+16x+16)`
`impliesx^(2)-8x-20=0`
`impliesx^(2)-10x+2x-20=0`
`impliesx(x-10)+2(x-10)=0`
`implies(x-10)(x+2)=0`
`impliesx=10orx=-2`
`impliesx=10" "(`because`"length cannot be negative")`
So, length of the shortest side =10 metres
length of the hypotenuse `=(2xx10+6)=26` metres
and length of the third side `=(2xx10+4)=24` metres
Hence, sides of the triangle are 10m, 24m and 26m.