Question

Find the value of x. Circle geometry.

Answer 1

x = 18

By Pythagoras Theorem:

`{(x + 7)}^(2) = {(7)}^(2) + {(24)}^(2) \\ \\ \implies \: (x + 7)^(2) = 49 + 576 \\ \\ \implies \: (x + 7)^(2) = 625\\ \\ \implies \: x + 7 = \pm √(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 \\eq \: - 32 \\ \implies \: x = 18`