Question

triangle hij is similar to triangle klm. find the measure of side kl. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle HIJ\sim\triangle KLM\), the ratios of their corresponding sides are equal. That is \(\frac{IJ}{LM}=\frac{HI}{KL}\).

Step2: Substitute the known values

We know \(IJ = 59\), \(LM=29\), and \(HI = 28.1\). Let \(KL=x\). Then \(\frac{59}{29}=\frac{28.1}{x}\).

Step3: Solve for \(x\)

Cross - multiply gives \(59x=29\times28.1\). So \(x=\frac{29\times28.1}{59}\).
Calculate \(29\times28.1 = 814.9\). Then \(x=\frac{814.9}{59}\approx14.0\).

Answer:

\(14.0\)