Question

The hypotenuse of a right-angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.

Answer 1

let the shorter side be x m

Therefore hypotenuse = 2x-1

and third side = x + 1

by pythagorus theorem

$(2x-1{)}^2=x^2+(x+1{)}^2$

$4x^2+1-4x=x^2+x^2+1+2x$

$4x^2-4x+1=2x^2+2x+1$
$2x^2-6x=0$
$2x(x-3)=0$
$x-3=0$
$x=3$

then
use x=3
hypotenuse $=2x-1=2\times 3-1=5m$
third side = x+1=3+1=4m