Question

1. triangle ijk is similar to triangle lmn. find mn. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since $\triangle IJK\sim\triangle LMN$, the ratios of corresponding sides are equal. Let's assume the side - length of $IJ$ corresponds to the side - length of $LM$, and the side - length of $JK$ corresponds to the side - length of $MN$. So we have $\frac{JK}{MN}=\frac{IJ}{LM}$. Let $JK = 9$, $IJ = 17$, and $LM = 35$. We need to find $MN=x$. The proportion is $\frac{9}{x}=\frac{17}{35}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{9}{x}=\frac{17}{35}$ gives us $17x=9\times35$.

Step3: Solve for $x$

First, calculate $9\times35 = 315$. Then we have the equation $17x = 315$. Divide both sides by 17: $x=\frac{315}{17}\approx18.5$.

Answer:

$18.5$