Playground dimensions

Question

Authority wants to build a rectangular playground in one of their parks. The border of the playground is between 100 and 120 feet. The length of the playground is 2 feet longer than the width. The area of the playground needs to be between 700 and 800 square feet in order to fit the playground equipment. What are the possible dimensions of the playground if they can only buy supplies by the foot?

Answer 1

I believe the upper bound should be 27 × 29. As shown in the table below, 28 × 30 would provide an area of 840 square feet which is more than the limit of 800 square feet. 27 × 29 = 783 square feet meets the requirements.

Answer 2

Draw a rectangle. Make the width W, Make the length (W + 2).

Now from the words the border is to be between 100 and 120 feet. So

Add all the sides to get the border. W + W + (W + 2) + (W + 2)

Simplified and bounded makes. 100 ≤ 4 W + 4 ≤ 120

Subtracting 4 from all three sections of this inequality gives. 96 ≤ 4W ≤ 116

Dividing all sections by 4 gives 24 ≤ W ≤ 29

Now find the length by adding 2 to each dimension 26 ≤ L ≤ 31

This information gives us a list of possible dimensions. But not all the dimensions will give an area between 700 and 800.

24 X 26 = 624

25 X 27 = 675

26 X 28 = 728

27 X 29 = 783

28 X 30 = 840

Hope this helps.

No point in continuing. The area will be too large. The answers are. 26 X 28 or 28 X 30.