Question

question. triangle ljk is similar to triangle lmn. find the measure of side lm. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up proportion

Since $\triangle LJK\sim\triangle LMN$, the ratios of corresponding - sides are equal. That is, $\frac{LJ}{LM}=\frac{LK}{LN}$. Let $LM = x$. We know that $LJ = 17$, $LK = 13$, and $LN = 41$. So the proportion is $\frac{17}{x}=\frac{13}{41}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{17}{x}=\frac{13}{41}$ gives us $13x=17\times41$.

Step3: Calculate the right - hand side

First, calculate $17\times41 = 697$. So the equation becomes $13x = 697$.

Step4: Solve for $x$

Divide both sides of the equation $13x = 697$ by 13: $x=\frac{697}{13}\approx53.6$.

Answer:

$53.6$