Question

in the diagram below, $\triangle cde \sim \triangle fge$. find $n$.
(diagram: right triangle $fge$ with right angle at $g$, $ge = 8$ yd, hypotenuse $fe = 10$ yd; right triangle $cde$ with right angle at $d$, $ce = 5$ yd, $de = n$ yd)
write your answer as a whole number or a decimal. do not round.
$n = \square$ yards
submit

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle CDE\sim\triangle FGE\), the ratios of corresponding sides are equal. That is \(\frac{CE}{FE}=\frac{DE}{GE}\).
We know \(CE = 5\) yd, \(FE=10\) yd, \(GE = 8\) yd and \(DE=n\).
Substituting the values into the proportion \(\frac{5}{10}=\frac{n}{8}\).

Step2: Solve the proportion for \(n\)

Cross - multiply: \(10n=5\times8\).
First, calculate \(5\times8 = 40\). So, \(10n = 40\).
Then divide both sides by 10: \(n=\frac{40}{10}\).

Answer:

\(n = 4\) yards