JAMB 1983 · UME · Q16

The lengths of the sides of a right-angled triangle are $(3x + 1)$ cm, $(3x - 1)$ cm and $x$ cm. Find $x$ .

Worked solution (try it first)

The longest side, $3x + 1$ , is the hypotenuse.
By Pythagoras, $(3x + 1)^2 = (3x - 1)^2 + x^2$ .
Expand both brackets: $9x^2 + 6x + 1 = 9x^2 - 6x + 1 + x^2$ .
Cancel $9x^2$ and 1 from both sides and collect the $x$ terms: $12x = x^2$ , so $x(x - 12) = 0$ .
A side can't be 0 cm, so $x = 12$ (sides 12, 35 and 37), option D.