Question

The hypotenuse of a right angled triangle is 6 metres more than twice the shortest side.

Answer 1

Let the shortest side be $x$

Then, Hypotenuse $=2x+6$ and third side $=2x+6-2$

Third side $=2x+4$

Since, we know that

$Hypotenus{e}^2=Bas{e}^2+prependicula{r}^2$

Therefore,

${(2x+4)}^2+x^2={(2x+6)}^2$

$\Rightarrow 4x^2+16+16x+x^2=4x^2+36+24x$

$\Rightarrow x^2+16x-24x+16-36=0$

$\Rightarrow x^2-8x-20=0$

$\Rightarrow x^2-(10-2)x-20=0$

$\Rightarrow x^2-10x+2x-20=0$

$\Rightarrow x(x-10)+2(x-10)=0$

$\Rightarrow (x-10)(x+2)=0$

$\Rightarrow x-10=0$ or $x+2=0$

$\Rightarrow x=10$ or $x=-2$ (not exits)

Therefore,

Shortest side $x=10m$

Hypotenuse $=2x+6=2\times 10+6=26m$

Third side $=2x+4=2\times 10+4=24m$

Hence, this is the answer.