Question

Which of the following is true about the area and perimeter of rectangles? A Two rectangles with the same area must have the same perimeter. B Two rectangles with the same perimeter must have the same area. C Two rectangles with the same perimeter can have different areas. D No two rectangles can have the same area.

Answer 1

The correct answer is C



A states that two rectangles with the same area must have the same perimeter, but this is false.

Let’s say you have a rectangle that has an area of 12 Sq ft

It could be 4 x 3 or 6 x 2

Given that our perimeter is 2l x 2w = p:

8 + 6 = 14 but 12 + 4 = 16



B says that’s two rectangles with the same perimeter must have the same area, this is also false.

Let’s take our perimeter of 16 for example.

We could have a rectangle of 2 x 6 and we could have a rectangle of 4 x 4

However, 2 x 6 has an area of 12
Meanwhile, 4 x 4 has an area of 16



C says that two rectangles with the same perimeter can have different areas. I already proved this with the last one


D says that no two rectangles can have the same area

4 x 3 and 6 x 2 both have an area of 12