Marni wants to fence in a rectangular are of 48 ft squared. she wants to but the least amount of fencing.
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?
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
To determine the dimensions Marni should use to build the rectangular area with the least amount of fencing, we need to find two whole numbers whose product is equal to 48. Listing out the factors of 48, we have: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
To minimize the amount of fencing, we should choose dimensions that are as close to each other as possible. The closest pair is 6 and 8, as their product equals 48.
Therefore, the dimensions she should use to build the rectangular area with the least amount of fencing are 6 feet by 8 feet.
To find out how much fencing she will need, we need to calculate the perimeter of the rectangular area. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Plugging in the values, we have P = 2(6) + 2(8) = 12 + 16 = 28 feet.
So, Marni will need 28 feet of fencing to enclose the rectangular area with the dimensions of 6 feet by 8 feet.
I found this answer by considering all the factors of 48 and choosing the pair of dimensions that are closest together. Then, I calculated the perimeter using the formula and determined the amount of fencing required.