Question

quadrilateral fghi is similar to quadrilateral jklm. find the measure of side lm. round your answer to the nearest tenth if necessary. figures are not drawn to scale. i h 29 l m 43 8 k j f g

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals \(FGHI\) and \(JKLM\) are similar, their corresponding sides are proportional. Let's assume \(IH\) corresponds to \(JM\) and \(IF\) corresponds to \(LM\). So, \(\frac{IH}{JM}=\frac{IF}{LM}\).

Step2: Substitute known values

We know \(IH = 29\), \(IF = 43\), and \(JM = 8\). Substituting these into the proportion: \(\frac{29}{8}=\frac{43}{LM}\).

Step3: Solve for \(LM\)

Cross - multiply to get \(29\times LM=43\times8\). Then \(LM=\frac{43\times8}{29}\). Calculate \(43\times8 = 344\), so \(LM=\frac{344}{29}\approx11.9\).

Answer:

\(11.9\)