Answer:
6√2
Step-by-step explanation:
ΔEBD and ΔEDC are similar. Therefore the sides are in proportion:
[tex]\dfrac{DE}{EB}=\dfrac{EC}{DE}[/tex]
We have:
DE = a
EB = 18
EC = 4
Substitute:
[tex]\dfrac{a}{18}=\dfrac{4}{a}[/tex] cross multiply
[tex](a)(a)=(18)(4)\\\\a^2=72\to a=\sqrt{72}\\\\a=\sqrt{36\cdot2}\\\\a=\sqrt{36}\cdot\sqrt2\\\\a=6\sqrt2[/tex]
