Question

1. the following shapes are similar. $overline{ab} : overline{ij}$ is 5:1 and the length of $overline{fe}$ is 30. what is the length of $overline{nm}$?

options: 150, 6, 5, 125

Explanation:

Step1: Identify corresponding sides

Since the shapes are similar, corresponding sides are proportional. $\overline{FE}$ and $\overline{NM}$ are corresponding sides, and the ratio of $\overline{AB}$ to $\overline{IJ}$ is $5:1$, so the scale factor of the first shape to the second is $5:1$. Wait, actually, if $\overline{AB} : \overline{IJ} = 5:1$, then the first shape (with $\overline{AB}$) is larger than the second (with $\overline{IJ}$) by a scale factor of 5. But we need to find the length of $\overline{NM}$, which corresponds to $\overline{FE}$. Wait, maybe I got the ratio reversed. Let's think again: similar figures, so the ratio of corresponding sides is equal. Let the length of $\overline{NM}$ be $x$. The ratio of $\overline{FE}$ to $\overline{NM}$ should be equal to the ratio of $\overline{AB}$ to $\overline{IJ}$, which is $5:1$. So $\frac{FE}{NM} = \frac{5}{1}$. We know $FE = 30$, so $\frac{30}{x} = \frac{5}{1}$.

Step2: Solve for $x$

Cross - multiply: $5x = 30\times1$. Then $x=\frac{30}{5}=6$.

Answer:

6