IXL | Rectangles: relationship between perimeter and area

The rectangles below have the same perimeter.

6 ft

8 ft

If the area of the red rectangle is 33 square feet, what are its dimensions?

feet by feet

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Learn with an example

question

The rectangles below have the same perimeter.

6 ft

4 ft

If the area of the green rectangle is 21 square feet, what are its dimensions?

feet by feet

key idea

Rectangles with the same perimeter can have different areas.

solution

Find the perimeter of the yellow rectangle.

6 + 4 + 6 + 4 = 20

The green rectangle has a perimeter of 20.

Next make a list of possible dimensions for the green rectangle. The problem says that the green rectangle has an area of 21, so list dimensions that give an area of 21. The first whole number that divides evenly into 21 is 1, so start with 1 by 21.

Dimensions	Area	Perimeter
1 by 21	1 × 21 = 21
3 by 7	3 × 7 = 21

Next find the perimeters.

Dimensions	Area	Perimeter
1 by 21	1 × 21 = 21	1 + 21 + 1 + 21 = 44
3 by 7	3 × 7 = 21	3 + 7 + 3 + 7 = 20

Our very first calculation showed that the green rectangle has a perimeter of 20. So, its dimensions must be 3 by 7.

The green rectangle is 3 feet by 7 feet.

Looking for more? Try these:

Lesson: Area of rectangles

Lesson: Perimeter

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Teacher tools

Work it out

Not feeling ready yet? These can help:

II.9Relationship between area and perimeter

GG.1Perimeter

GG.2Area of rectangles and squares

AA.10Solve one-step equations with whole numbers

Lesson: Area of rectangles

Lesson: Perimeter

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