Question

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

Answer 1

Let the length of the shortest side be $x$ meters.

Then, hypotenuse$=(2x+6)$ metres

And the third side $(2x+6-2)$ metre$=(2x+4)$ metres

By Pythagoras theorem, we have

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

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

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

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

$\Rightarrow x=10orx=-2$

$\because$ $x$ can not be a negative $\therefore

$\Rightarrow x=10$

Length of the shortest side $=10$ metres

Length of the hypotenuse $=(2x+6)$ metres$=26$ metres

Length of the third side $=(2x+4)$ metres$=24$ metres

Hence the sides of the triangle are $10m,26m$ and $24m$