Question

quadrilateral ghij is similar to quadrilateral klmn. find kl. round your answer to the nearest tenth if necessary. figures are not drawn to scale. j 17 i g 26 h m 59 l n x k

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals \( GHIJ \) and \( KLMN \) are similar, their corresponding sides are proportional. Side \( JI \) (length 17) corresponds to side \( MN \) (length 59), and side \( GH \) (length 26) corresponds to side \( KL \) (length \( x \)).

Step2: Set up proportion

The proportion of corresponding sides is \( \frac{JI}{MN} = \frac{GH}{KL} \). Substituting the known values: \( \frac{17}{59} = \frac{26}{x} \).

Step3: Solve for \( x \)

Cross - multiply to get \( 17x = 59\times26 \). First, calculate \( 59\times26 = 1534 \). Then, solve for \( x \) by dividing both sides by 17: \( x=\frac{1534}{17}\approx90.2 \).

Answer:

\( 90.2 \)