Question

quadrilateral ghij is similar to quadrilateral klmn. find the measure of side nk. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up proportion

Since the quadrilaterals are similar, the ratios of corresponding sides are equal. Let $NK = x$. The ratio of the side corresponding to $NK$ in the first - quadrilateral is $GJ$. So, $\frac{NK}{GJ}=\frac{ML}{IH}$.

Step2: Substitute values

We know that $GJ = 13.4$, $ML = 25$, and $IH = 8$. Substituting these values into the proportion $\frac{x}{13.4}=\frac{25}{8}$.

Step3: Solve for x

Cross - multiply to get $8x=13.4\times25$. Then $8x = 335$. Divide both sides by 8: $x=\frac{335}{8}=41.875$.

Step4: Round the answer

Rounding $41.875$ to the nearest tenth gives $41.9$.

Answer:

$41.9$