Question

What is the value of a? 9

Answer 1

ΔBED and Δ DEC are similar (AAA). Therefore we have the proportion:

$\dfrac{a}{18}=\dfrac{4}{a}$      cross multiply

$a^2=(18)(4)\\\\a^2=72\to a=\sqrt{72}\\\\a=\sqrt{36\cdot2}\\\\a=\sqrt{36}\cdot\sqrt2\\\\\boxed{a=6\sqrt2}$