Question

The sides of a right-angled triangle have lengths (x-3)cm, (x+11) cm and 2xcm, where 2x is the hypothenuse. Find x

Answer 1

por pitagoras :

$(x - 3)^{2} + (x + 11)^{2} = (2x) ^{2} \\ \\ {x}^{2} - 6x + 9 + {x}^{2} + 22x + 121 = 4 {x}^{2}$
$2 {x}^{2} - 4 {x}^{2} + 16x + 130 = 0$
$- 2 {x}^{2} + 16x + 130 = 0$
usando formula resolvente te queda

$x = 13 \\ x = - 5$
como x no puede ser negativo

$x = 13$