Question

triangle klm is similar to triangle nop. find pn. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
m to l is 12, m to k is 7, o to p is 59, p to n is x

Explanation:

Step1: Identify corresponding sides

Since $\triangle KLM \sim \triangle NOP$, the corresponding sides are proportional. So, $\frac{KM}{PN}=\frac{LM}{ON}$.
We know $KM = 7$, $LM = 12$, and $ON = 59$. Let $PN = x$.

Step2: Set up the proportion

Substitute the known values into the proportion: $\frac{7}{x}=\frac{12}{59}$.

Step3: Cross - multiply to solve for $x$

Cross - multiplying gives $12x=7\times59$.
Calculate $7\times59 = 413$. So, $12x = 413$.
Then, $x=\frac{413}{12}\approx34.4$.

Answer:

$\approx34.4$