Question

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.
answer attempt 1 out of 2

Explanation:

Step1: Set up the proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let \( LI=x \). We have the proportion \( \frac{LI}{HE}=\frac{LK}{HG} \). Substituting the given values: \( \frac{x}{20}=\frac{41 + 11}{11} \).

Step2: Simplify the right - hand side

First, calculate \( 41+11 = 52 \). So the proportion becomes \( \frac{x}{20}=\frac{52}{11} \).

Step3: Solve for \( x \)

Cross - multiply: \( 11x=20\times52 \). Then \( 11x = 1040 \). Divide both sides by \( 11 \): \( x=\frac{1040}{11}\approx81.8 \).

Answer:

\( 81.8 \)