Verified Answer :

MissPhiladelphia

Hi, thank you for posting your question.

This problem can be solved through ratio and proportion which can be applied to similar triangles like that shown in the figure. By ratio and proprotion,

AQ/AC = AP/AB
x/(40+x) = 7/(35+7)

Thus, x = 8

calculista

Answer:

Option A \(x=8\ units\)

Step-by-step explanation:

we know that

The triangles ABC and APQ are similar

then

The ratio of their corresponding sides is equal

\(\frac{AP}{AB}=\frac{AQ}{AC}\)

we have

\(AP=7\ units\)

\(AB=35+7=42\ units\)

\(AQ=x\ units\)

\(AC=(40+x)\ units\)

substitute

\(\frac{7}{42}=\frac{x}{(40+x)}\\ \\\frac{1}{6}=\frac{x}{(40+x)}\\ \\ 40+x=6x\\ \\6x-x=40\\ \\5x=40\\ \\x=8\ units\)

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