Question

find the missing length. the triangles in each pair are similar.

1. △lmn~△efg
2. △cde~△clm

lm =
cl =

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle LMN\sim\triangle EFG\), the ratios of corresponding sides are equal. That is \(\frac{LM}{EF}=\frac{MN}{FG}\). Given \(FG = 18\), \(EF=27\), \(MN = 30\). Let \(LM=x\). Then \(\frac{x}{27}=\frac{30}{18}\).

Step2: Solve the proportion

Cross - multiply: \(18x=30\times27\). So \(x=\frac{30\times27}{18}\). Calculate \(30\times27 = 810\), then \(x=\frac{810}{18}=45\).

For \(\triangle CDE\sim\triangle CLM\), the ratios of corresponding sides are equal. That is \(\frac{CL}{CD}=\frac{CM}{CE}\). Given \(CD = 88\), \(CE = 96\), \(CM = 36\). Let \(CL = y\). Then \(\frac{y}{88}=\frac{36}{96}\).

Step3: Solve the proportion

Cross - multiply: \(96y=36\times88\). So \(y=\frac{36\times88}{96}\). Calculate \(36\times88 = 3168\), then \(y=\frac{3168}{96}=33\).

Answer:

\(LM = 45\), \(CL=33\)