Question

What is the value of a?

Answer 1

6√2

Explanation:

ΔEBD and ΔEDC are similar. Therefore the sides are in proportion:

`(DE)/(EB)=(EC)/(DE)`

We have:

DE = a

EB = 18

EC = 4

Substitute:

`(a)/(18)=(4)/(a)` cross multiply

`(a)(a)=(18)(4)\\\\a^2=72\to a=√(72)\\\\a=√(36\cdot2)\\\\a=√(36)\cdot\sqrt2\\\\a=6\sqrt2`

Answer 2

a^2 = 18 * 4

a^2 = 72

a = 6√2