Question

Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side LM. Round your answer to the nearest tenth if necessary. I M 5 J H N L 34 G K 圖

Answer 1

$LM=24.3$

Explanation

Step 1

As the quadrilaterals are similar, the ratio of both of the sides must be equal,so

$\begin{gathered} ratio=\frac{green\text{ length}}{\text{red length}} \\ \end{gathered}$

so

$\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{7}{5}=\frac{34}{LM} \end{gathered}$

Step 2

solve for LM

$\begin{gathered} \frac{7}{5}=\frac{34}{LM} \\ \text{cross multiply} \\ 7\cdot LM=34\cdot5 \\ 7\cdot LM=170 \\ \text{divide both sides by 7} \\ \frac{7\cdot LM}{7LM}=\frac{170}{7} \\ LM=24.285 \\ \text{rounded to the nearest tenth} \\ LM=24.3 \end{gathered}$

I hope this helps you