In a right-angled triangle, one of the shorter sides is 7 cm longer than the other, and the hypotenuse is 13 cm. How long is the shortest side?

Explanation

1. 01

   Let the shortest side be $x$ cm; the other is $x + 7$ cm. By Pythagoras, $x^2 + (x + 7)^2 = 169$.

2. 02

   $2x^2 + 14x + 49 = 169$, so $x^2 + 7x - 60 = 0$.

3. 03

   $(x + 12)(x - 5) = 0$; a length is positive, so $x = 5$ cm.

4. 04

   Check: $25 + 144 = 169$.