Question

quadrilateral fghi is similar to quadrilateral jklm. find the measure of side mj. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral FGHI ~ quadrilateral JKLM, corresponding sides are proportional. Side IH (length 8) corresponds to side LM (length 31), and side IF (length 13) corresponds to side MJ.

Step2: Set up proportion

Let \( x \) be the length of MJ. Then \(\frac{IH}{LM}=\frac{IF}{MJ}\), so \(\frac{8}{31}=\frac{13}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 8x = 31\times13 \). Calculate \( 31\times13 = 403 \). Then \( x=\frac{403}{8}=50.375\approx50.4 \).

Answer:

50.4