Question

One side of a right-angled triangle exceeds the other side by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter side of the triangle.

• A. 12 inches
• B. 7 inches
• C. 20 inches
• D. 14 inches

Answer 1

The correct option is A

12 inches

Let the sides of the right angle triangle be $xandx+4$
Applying Pythagoras theorem,
$x^2+(x+4{)}^2=(20{)}^2$
$x^2+x^2+8x+16=400$
$2x^2+8x-384=0$
$\Rightarrow$ $x^2+4x-192=0$
$\Rightarrow$ $x^2+16x-12x-192=0$
$\Rightarrow$ $x(x+16)-12(x+16)=0$
$\Rightarrow$ $(x+16)(x-12)=0$
$\Rightarrow$ $x=-16orx=12$
Since length cannot be negative, x = 12