Question

triangle ijk is similar to triangle lmn. find nl. 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 that side $IK$ corresponds to side $LN$ and side $IJ$ corresponds to side $LM$. So we have the proportion $\frac{IK}{LN}=\frac{IJ}{LM}$. Substituting the given values, $\frac{29}{x}=\frac{16}{55}$.

Step2: Cross - multiply

Cross - multiplying gives us $16x = 29\times55$.
$16x=1595$.

Step3: Solve for $x$

Divide both sides of the equation by 16: $x=\frac{1595}{16}=99.6875$.

Step4: Round to nearest tenth

Rounding $99.6875$ to the nearest tenth, we get $99.7$.

Answer:

$99.7$