Question

quadrilateral efgh is similar to quadrilateral ijkl. find li. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \(EFGH\) is similar to quadrilateral \(IJKL\), the corresponding sides are proportional. So, \(\frac{EH}{LI}=\frac{HG}{LK}\). We know \(EH = 20\), \(HG = 11\), and \(LK = 41\). Let \(LI=x\).

Step2: Set up the proportion

Substitute the known values into the proportion: \(\frac{20}{x}=\frac{11}{41}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives us \(11x=20\times41\). Calculate \(20\times41 = 820\), so the equation becomes \(11x = 820\).

Step4: Solve for \(x\)

Divide both sides of the equation by 11: \(x=\frac{820}{11}\approx74.5\) (rounded to the nearest tenth).

Answer:

\(LI\approx74.5\)