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