Question

The hypotenuse of a right triangle is $3m$ more than twice of the shortest side.
If the third side is $1m$ less than the hypotenuse. Find the shortest side?

Answer 1

Let shortest side $=x$ meter

Hypotenuse of right triangle $=(3+2x)$ meter

Third side of right triangle $=[1-(3+2x\left)\right]$ meter

By pythagoras theorem,

$(Hypotenuse{)}^2=(Shortestside{)}^2+(Thirdside{)}^2$

$(3+2x{)}^2=x^2+(1-(3+2x){)}^2$

$9+4x^2+12x=x^2+(-2-2x{)}^2$

$9+3x^2+12x=(2+2x{)}^2$

$9+3x^2+12x=4+4x^2+8x$

$-x^2+4x+5=0$

$x^2-4x-5=0$

$(x-5)(x+1)=0$

$x=5,-1$

$\therefore$ Shortest side $=5$ meter.