Question

If the sides of a right triangle are $x,x+1$ and $x-1$, then the hypotenuse is:

• A. $5$
• B. $4$
• C. $1$
• D. $0$

Answer 1

The correct option is A $5$

In a right $\Delta$, hypotenuse is the largest side.
$\therefore$ Hypotenuse $=x+1$
$\therefore (x+1{)}^2=x^2+(x-1{)}^2(Pyth.Th.)$
$\Rightarrow x^2+2x+1=x^2+x^2-2x+1$
$\Rightarrow x^2=4x$

$\Rightarrow x=4$ since $x=0$ is not possible
$\therefore$ Hypotenuse $=4+1=5$.

Hence, the hypotenuse is $5$.