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 $LK$ and side $HI$ corresponds to side $MK$. So we have the proportion $\frac{HJ}{LK}=\frac{HI}{MK}$. Substituting the given values, we get $\frac{31}{59}=\frac{17}{x}$.

Step2: Cross - multiply

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

Step3: Calculate the right - hand side

$17\times59 = 1003$. So, $31x=1003$.

Step4: Solve for $x$

Dividing both sides by 31, we have $x=\frac{1003}{31}\approx32.4$.

Answer:

$32.4$