Question

are these shapes similar?

Explanation:

Step1: Calculate the ratio of corresponding sides

For the first shape (rectangle \(FGHI\)) with sides \(25\) mi and \(40\) mi, and the second shape (rectangle \(RQPO\)) with sides \(20\) mi and \(32\) mi.
The ratio of the shorter sides: \(\frac{25}{20}=\frac{5}{4}\)
The ratio of the longer sides: \(\frac{40}{32}=\frac{5}{4}\)

Step2: Check angle - equality

Both shapes are rectangles. In a rectangle, all angles are \(90^{\circ}\). So, the corresponding angles of the two rectangles are equal.

Answer:

yes