Question

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

Explanation:

Step1: Set up proportion

Since the two quadrilaterals are similar, the ratios of corresponding sides are equal. Let the length of side $ML$ in the first quadrilateral be $20$, the length of the corresponding - side $KL$ in the second quadrilateral be $14.5$, and the length of side $GH$ in the first quadrilateral be $26$. Let the length of the corresponding side $MN$ (the side we want to find) be $x$. The proportion is $\frac{ML}{KL}=\frac{GH}{MN}$, or $\frac{20}{14.5}=\frac{26}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{20}{14.5}=\frac{26}{x}$ gives us $20x = 14.5\times26$.

Step3: Calculate the right - hand side

First, calculate $14.5\times26=377$. So, $20x = 377$.

Step4: Solve for $x$

Divide both sides of the equation $20x = 377$ by $20$. We get $x=\frac{377}{20}=18.85\approx18.9$.

Answer:

$18.9$