Question

find j.
write your answer as a whole number or a decimal. do not round.
$i = quad$ feet

Explanation:

Step1: Use the similarity of triangles

Since \( \triangle CBD\sim\triangle CFE\) (by AA similarity, as \( \angle CBD=\angle CFE = 90^{\circ}\) and \( \angle C\) is common), the ratios of corresponding sides are equal. That is \(\frac{CB}{CF}=\frac{BD}{FE}\). Also, \(CF = CB + BF=4 + 8=12\) feet, \(CB = 4\) feet, \(BD = 3\) feet. Let \(FE = j\).

Step2: Substitute values into the proportion

Substituting the values into \(\frac{CB}{CF}=\frac{BD}{FE}\), we get \(\frac{4}{12}=\frac{3}{j}\).
Cross - multiply: \(4j=3\times12\).

Step3: Solve for \(j\)

\(4j = 36\), then \(j=\frac{36}{4}=9\).

Answer:

\(9\)