Question

in the figure shown below, e and g lie on ac, d and f lie on ab, de and fg are parallel to bc, and the given lengths are in feet. what is the length of ac, in feet? a. 13 b. 26 c. 29 d. 42 e. 48

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(DE\parallel BC\), we have \(\frac{AD}{AB}=\frac{AE}{AC}\).
First, find \(AB = AD + DF+FB=8 + 7+6=21\).
Let \(AC=x\). Then \(\frac{AD}{AB}=\frac{AE}{AC}\), where \(AD = 8\), \(AB=21\), \(AE = 16\).
So, \(\frac{8}{21}=\frac{16}{x}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(8x=16\times21\).
Then \(x=\frac{16\times21}{8}\).
Simplify: \(x = 42\).

Answer:

D. 42