Question

What is AE?
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Answer 1

AE = 18 units

Explanation:

Δ AEB and Δ DEC are similar , then corresponding sides are in proportion, that is

`(AE)/(DE)` =
`(AB)/(DC)` , substitute values

`(2x+4)/(x+8)` =
`(12)/(10)` ( cross- multiply )

10(2x + 4) = 12(x + 8) ← distribute parenthesis on both sides

20x + 40 = 12x + 96 ( subtract 12x from both sides )

8x + 40 = 96 ( subtract 40 from both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Then

AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18 units