Question

pentagon abcde is similar to pentagon lmn pq. which proportion could we use to find the length of $overline{np}$? choose 1 answer: (a) $\frac{32}{58}=\frac{24}{y}$ (b) $\frac{40}{64}=\frac{24}{y}$ (c) $\frac{24}{32}=\frac{y}{64}$ (d) $\frac{24}{32}=\frac{y}{40}$

Explanation:

Step1: Recall similarity property

For similar polygons, the ratios of corresponding - side lengths are equal. Side $DE$ in pentagon $ABCDE$ corresponds to side $PQ$ in pentagon $LMNPQ$, and side $CD$ in pentagon $ABCDE$ corresponds to side $NP$ in pentagon $LMNPQ$.
The length of $DE = 32$, the length of $PQ = 24$, the length of $CD = 40$, and the length of $NP=y$.

Step2: Set up proportion

The proportion of corresponding - side lengths is $\frac{PQ}{DE}=\frac{NP}{CD}$, which is $\frac{24}{32}=\frac{y}{40}$.

Answer:

D. $\frac{24}{32}=\frac{y}{40}$