Question

quadrilateral ghij is similar to quadrilateral klmn. find the measure of side mn. round your answer to the nearest tenth if necessary. answer attempt 2 out of 2

Explanation:

Step1: Set up proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let the side corresponding to $MN$ in $GHIJ$ be $IJ = 23$, and the side corresponding to $NK$ in $GHIJ$ be $JG=32$. The length of $NK = 15.5$. The proportion is $\frac{MN}{IJ}=\frac{NK}{JG}$.

Step2: Substitute values

Substitute $IJ = 23$, $NK = 15.5$, and $JG = 32$ into the proportion: $\frac{MN}{23}=\frac{15.5}{32}$.

Step3: Solve for MN

Cross - multiply: $32\times MN=23\times15.5$. Then $32MN = 356.5$. Divide both sides by 32: $MN=\frac{356.5}{32}=11.140625\approx11.1$.

Answer:

$11.1$