Question

If the sides of a right triangle are consecutive natural numbers, then the length of the shortest side is units.

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

Let the length of the shortest side be $x-1$.
Hence , the length of the other two sides will be $x$ and $x+1$.

Since, the three sides form a right angle triangle,
$(x+1{)}^2=(x-1{)}^2+(x{)}^2$
$\Rightarrow$ $x^2-4x$ = 0

The roots of a quadratic equation $a{x}^2+bx+c=0$ is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Hence, the roots are $x=\frac{-(-4)\pm \sqrt{(-4{)}^2-4\times 1\times 0}}{2\times 1}$

$x=4or0$

Since, the length of a side cannot be 0, hence, $x$ = 4 units
So, $x-1$ = 4 - 1 = 3 units.
So, the length of the shortest side = 3 units.