Question

Look at the two shaded rectangles on the grid below. Which statement best compares the areas and the perimeters of the two rectangles?

Answer 1

The rectangles have different areas and different perimeters. Rectangle 1 has an area of 30 square units and a perimeter of 22 units, while Rectangle 2 has an area of 24 square units and a perimeter of 22 units.

To compare the areas and perimeters of the two rectangles, let's calculate these values:

Rectangle 1:

- Area =
`\(6 * 5 = 30\)` square units

- Perimeter =
`\(2 * (6 + 5) = 22\)` units

Rectangle 2:

- Area =
`\(8 * 3 = 24\)` square units

- Perimeter =
`\(2 * (8 + 3) = 22\)` units

Now, let's analyze the options:

A) The rectangles have equal areas and equal perimeters. (Incorrect, as the areas are different.)

B) The rectangles have equal areas and different perimeters. (Incorrect, as both the areas and perimeters are different.)

C) The rectangles have different areas and equal perimeters. (Incorrect, as both the areas and perimeters are different.)

D) The rectangles have different areas and different perimeters. (Correct, as the areas and perimeters are different.)

Therefore, the correct answer is:

D) The rectangles have different areas and different perimeters.