Question

in the diagram below, $\triangle edc \sim \triangle bac$. find $n$.

diagram of right triangle bac with right angle at a, ab = 6 m, and triangle edc with right angle at d, ed = 3 m, ec = 5 m, and bc = n

write your answer as a whole number or a decimal. do not round.
$n = \square$ meters

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle EDC\sim\triangle BAC\), the ratios of corresponding sides are equal. That is \(\frac{ED}{BA}=\frac{EC}{BC}\). Let \(BC = n\), \(EC = 5\), \(ED=3\), \(BA = 6\).

Step2: Set up the proportion

\(\frac{3}{6}=\frac{5}{n}\) (by the similarity of triangles \(\triangle EDC\) and \(\triangle BAC\)).

Step3: Cross - multiply

Cross - multiplying gives \(3n=6\times5\).

Step4: Solve for \(n\)

\(3n = 30\), then \(n=\frac{30}{3}\).

Answer:

\(10\)