Question

1. triangles lfg and lmn are similar.

what is the length of (overline{mn})?
a. 35 inches
b. 40 inches
c. 10 inches
d. 60 inches

Explanation:

Step1: Find the similarity ratio

Since triangles \(LFG\) and \(LMN\) are similar, the ratio of corresponding sides is equal. The side \(LM\) of \(\triangle LMN\) is \(15 + 30=45\) inches and the corresponding side in \(\triangle LFG\) is \(15\) inches. The ratio of similarity \(k=\frac{LM}{LF}=\frac{45}{15} = 3\).

Step2: Use the ratio to find \(MN\)

Let \(MN=x\). We know that the side \(FG = 20\) inches in \(\triangle LFG\) and \(MN\) in \(\triangle LMN\) is the corresponding side. Using the similarity ratio \(k\), we have \(x=k\times FG\). Substituting \(k = 3\) and \(FG=20\) inches, we get \(x = 3\times20\).

Answer:

B. 40 inches