What is the value of X?

Mathematics

1 answer:

Ugo [173]3 years ago

4 0

∆ABC similar to ∆CBD

DB/AC = CB/AB

$\frac{x}{7.5} = \frac{7.5}{x + 3} \\ x(x + 3) = {7.5}^{2} = { (\frac{15}{2}) }^{2} \\ {x}^{2} + 3x = \frac{225}{4} \\ 4 {x}^{2} + 12x = 225 \\ 4 {x}^{2} + 12x + 9 = 216 \\ {(2x + 3)}^{2} = 216 \\ 2x + 3 = 6 \sqrt{6} \\ x = - 1.5 + 3 \sqrt{6}$

approximately 6.1485

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