Question

find the length of \\(\overline{eg}\\).
triangle diagram with points e, g, f, h, d; gf=6, fh=5, dh=7.5; options a) 9, b) 7, c) 15, d) 12; radio buttons for a, b, c, d

Explanation:

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

Since \( GH\parallel ED\), we have \(\frac{FG}{GE}=\frac{FH}{HD}\). Let \(EG = x\). Then \(\frac{6}{x}=\frac{5}{7.5}\) (by the ratio of corresponding segments of parallel - cut transversals).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(5x=6\times7.5\). So \(5x = 45\).

Step3: Divide both sides by 5

Dividing both sides of \(5x = 45\) by 5, we get \(x=\frac{45}{5}=9\).

Answer:

A. 9