Answer:
x = 18
By Pythagoras Theorem:
[tex] {(x + 7)}^{2} = {(7)}^{2} + {(24)}^{2} \\ \\ \implies \: (x + 7)^{2} = 49 + 576 \\ \\ \implies \: (x + 7)^{2} = 625\\ \\ \implies \: x + 7 = \pm \sqrt{625}\\ \\ \implies \: x + 7 = \pm \: 25\\ \\ \implies \: x + 7 = 25 \: \: or \: \: x + 7 = - 25 \\ \\ \implies \: x = 25 - 7 \: \: or \: \: x = - 25 - 7 \\ \\ \implies \: x = 18 \: \: or \: \: x = - 32 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \neq \: - 32 \\ \implies \: x = 18[/tex]
