Question

The sides of a right triangle are $(x-1)$, $x$ and $(x+1)$. Find the sides of the triangle.

• A. $3,4,5$
• B. $5,5,6$
• C. $2,3,4$
• D. None of these

Answer 1

The correct option is A $3,4,5$

The sides of a triangle given are $x-1,x$ and $x+1.$

$\because x+1>x>x-1,$ $\forall x>0$

$⟹$ $x+1$ is the longest side
As it is a right angled triangle, we apply Pythagoras theorem
therefore,
${(x-1)}^2+x^2={(x+1)}^2$
$\Rightarrow x^2-2x+1+x^2=x^2+2x+1$
$\Rightarrow x^2-4x=0$
$\Rightarrow x(x-4)=0$
$x=4$ ,$x=0$

$x=0$ cannot be the side of a triangle.
One side is $4.$
Other two sides
$x-1=4-1=3$
$x+1=4+1=5$
$\therefore$ Sides of a triangle are $3,4$ and $5.$
Answer is option $\text{A}$