Question

question
quadrilateral fghi is similar to quadrilateral jklm. find kl. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
answer attempt 1 out of 2

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals \(FGHI\) and \(JKLM\) are similar, their corresponding sides are proportional. The side \(HI = 7\) in \(FGHI\) corresponds to side \(LM = 27\) in \(JKLM\), and side \(GH = 4\) in \(FGHI\) corresponds to side \(KL = x\) in \(JKLM\).

Step2: Set up proportion

The proportion of corresponding sides is \(\frac{HI}{LM}=\frac{GH}{KL}\). Substituting the known values, we get \(\frac{7}{27}=\frac{4}{x}\).

Step3: Solve for \(x\)

Cross - multiply to get \(7x = 4\times27\). Then \(7x=108\). Divide both sides by 7: \(x=\frac{108}{7}\approx15.4\) (rounded to the nearest tenth).

Answer:

\(15.4\)