Question

If the hypotenuse of a right-angled triangle is 10 inches, and one leg of the triangle exceeds the other by 2 inches, then the shorter leg measures .

• A. 4 inches
• B. 2 inches
• C. 8 inches
• D. 6 inches

Answer 1

The correct option is D 6 inches

Let the lengths of the shorter and longer legs of the right-angled triangle be $x$ and $x+2$ inches respectively.


Applying Pythagoras' theorem, we have
$x^2+(x+2{)}^2={10}^2.$
$⟹x^2+x^2+4x+4=100$
$2x^2+4x-96=0$
$\Rightarrow x^2+2x-48=0$
i.e., $x^2+8x-6x-48=0$
$\Rightarrow x(x+8)-6(x+8)=0$
$\Rightarrow (x+8)(x-6)=0$
Thus, the roots of the equation are 6 and -8.
Since length cannot be negative, we have the shorter side of the triangle to be equal to $x=6$ inches.