Question

triangle hij is similar to triangle klm. find mk. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let's assume that side $HJ$ corresponds to side $MK$ and side $HI$ corresponds to side $LK$. So we have the proportion $\frac{HJ}{MK}=\frac{HI}{LK}$. Substituting the given values, we get $\frac{31}{x}=\frac{17}{59}$.

Step2: Cross - multiply

Cross - multiplying gives us $17x = 31\times59$.

Step3: Calculate the right - hand side

$31\times59=1829$. So the equation becomes $17x = 1829$.

Step4: Solve for $x$

Dividing both sides of the equation by 17, we have $x=\frac{1829}{17}\approx107.6$.

Answer:

$107.6$