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3 years ago

What is AE? Enter your answer in the box?

Mathematics

1 answer:

Nataly [62]3 years ago

5 0

Answer:

AE = 18 units

Step-by-step explanation:

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

$\frac{AE}{DE}$ = $\frac{AB}{DC}$ , substitute values

$\frac{2x+4}{x+8}$ = $\frac{12}{10}$ ( 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

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