Question

triangle ijk is similar to triangle lmn. find the measure of side lm. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since \(\triangle IJK\sim\triangle LMN\), the ratios of corresponding sides are equal. Let \(LM = x\). The ratio of \(IK\) to \(LN\) is equal to the ratio of \(IJ\) to \(LM\). So, \(\frac{IK}{LN}=\frac{IJ}{LM}\). Substituting the values \(IK = 4\), \(LN=20.8\), \(IJ = 2\) and \(LM=x\), we get \(\frac{4}{20.8}=\frac{2}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(4x=2\times20.8\).

Step3: Solve for \(x\)

First, calculate \(2\times20.8 = 41.6\). Then, \(4x = 41.6\). Divide both sides by \(4\): \(x=\frac{41.6}{4}\).

Answer:

\(10.4\)