Question

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

Answer 1

$A{B}^2+A{C}^2=B{C}^2$

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

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

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

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

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

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

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

$\therefore x\ne -2$, $x=10$

[side cannot be negative]

Therefore, sides are Hypotenuse$=6+2\left(10\right)=26$

Base$=10$

Perpendicular$=4+2\left(10\right)=24$.