Question

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

• A. $24$ m
• B. $34$ m
• C. $26$ m
• D. $10$ m

Answer 1

The correct option is C $26$ m

Let the shortest side of the triangle be $x$ M.
Then, hypotenuse$=(2x+6)$ m
Third side$=(2x+6)-2=(2x+4)$ m
By Pythagoras' Theorem,
${(2x+6)}^2={(2x+4)}^2+x^2$
$\Rightarrow$ $4x^2+24x+36=4x^2+16x+16+x^2$
$\Rightarrow$ $x^2-8x-20=0$
$\Rightarrow$ $x^2-10x+2x-20=0$
$\Rightarrow$ $(x-10)(x+2)=0$
$\Rightarrow$ $x=10$ or $-2$
$\therefore$ $x$ cannot be negative, $x=10$
Hypotenuse$=(2\times 10+6)$ m$=26$ m