Question

1. a farmer is planning to fence in a larger plot of land for her cows and a smaller plot of land for her goats. 24 ft 32 ft 18 ft 24 ft are these similar shapes? explain.

Explanation:

Step1: Find the ratio of corresponding sides

For the larger rectangle with sides 32 ft and 24 ft, and the smaller rectangle with sides 24 ft and 18 ft. The ratio of the longer - sides is $\frac{32}{24}=\frac{4}{3}$, and the ratio of the shorter - sides is $\frac{24}{18}=\frac{4}{3}$.

Step2: Check similarity condition

Two rectangles are similar if the ratios of their corresponding sides are equal. Since the ratios of the corresponding sides of the two rectangles are equal ($\frac{4}{3}$ for both pairs of corresponding sides), the rectangles are similar.

Answer:

Yes, the two rectangles are similar because the ratios of their corresponding sides are equal.