Question

How do I find x in this question?

Answer 1

x = 8

Explanation:

By Basic Proportionality Theorem:

`(3)/(x - 2) = (x)/(x + 8) \\ \\ x(x - 2) = 3(x + 8) \\ \\ {x}^(2) - 2x = 3x + 24 \\ \\ {x}^(2) - 2x - 3x - 24 = 0 \\ \\ {x}^(2) - 5x - 24 = 0 \\ \\ {x}^(2) - 8x + 3x - 24 = 0 \\ \\ x (x - 8) + 3(x - 8) = 0 \\ \\ (x - 8)(x + 3) = 0 \\ \\ x - 8 = 0 \: \: or \: \: x + 3 = 0 \\ \\ x = 8 \: \: or \: \: x = - 3 \\ \\ \because \: length \: can \: not \: be \: - ve \\ \\ \implies \: x \\eq - 3 \\ \\ \implies \: x = 8`