Question

question
quadrilateral fghi is similar to quadrilateral jklm. find the measure of side lm. round your
answer to the nearest tenth if necessary.

Explanation:

Step1: Use the property of similar polygons

For similar polygons, the ratios of corresponding sides are equal. So, \(\frac{GH}{KL}=\frac{FG}{JK}\). But here, since \(FGHI\sim JKLM\), the ratio of \(HI\) to \(LM\) is equal to the ratio of \(FG\) to \(JK\). Let \(LM = x\). Then \(\frac{HI}{LM}=\frac{FG}{JK}\).

Step2: Substitute the values

We know \(HI = 16\), \(FG=7\), \(JK = 26\). Substituting into \(\frac{16}{x}=\frac{7}{26}\).
Cross - multiply: \(7x=16\times26\).

Step3: Solve for \(x\)

First, calculate \(16\times26 = 416\). Then \(x=\frac{416}{7}\approx59.4\).

Answer:

\(59.4\)