Question

One leg of a right-angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg 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 length of triangle legs x and x+4.

Applying Pythagoras theorem,

$x^2+(x+4{)}^2=(20{)}^2$
$x^2+x^2+16+8x=400$
$2x^2+8x-384=0$
$x^2+4x-192=0$

we get x = -16 and x = 12

Length can't be negative.
Hence, $x=12$