Marni wants to fence in a rectangular are of 48 ft squared. she wants to but the least amount of fencing.

Question

1. Describe the dimensions she should us to build the are. use whole numbers only
2. How much fencing wil she need
3. Explain how you found that answer?

Answer 1

I largest area of a rectangle is obtained when that rectangle is a square, so
x^2 = 48
x = √48 = 4√3 = appr 6.9 or 7 as a whole number.

She will need 4(7) or 28 ft of fencing

If the rectangle is 6 ft by 8 ft, then the area will be exactly 48 ft^2
and the perimeter would be 2(6) + 2(8) = 28 ft

notice that if the rectangle is 7 by 7, we get an area of 49 ft^2, so using the same perimeter as the 6 by 8 rectangle we get a larger area.

Either way, the least amount of fencing she needs is 28 ft