What is the least perimeter of a rectangle with an area of 32 square feet?
least perimeter will be a square. So, what are the sides of such a square?
1 * 32
2 * 16
4 * 8
P = 2L + 2W
Which of those dimension will produce the smallest perimeter?
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To find the least perimeter of a rectangle with a specific area, you need to understand the relationship between the dimensions of a rectangle and its perimeter.
Let's denote the length of the rectangle as L and the width as W. The formula for the area A of a rectangle is given by A = L * W, and the formula for the perimeter P is given by P = 2L + 2W.
In this case, you are given that the area A is 32 square feet. So, you have the equation A = L * W = 32. Now, you need to find the values of L and W that minimize the perimeter P.
To solve this, let's list the possible pairs of length and width that multiply to give 32:
1,32
2,16
4,8
Now, for each pair, calculate the perimeter P using the formula P = 2L + 2W:
For the first pair (1,32):
P = 2(1) + 2(32) = 2 + 64 = 66
For the second pair (2,16):
P = 2(2) + 2(16) = 4 + 32 = 36
For the third pair (4,8):
P = 2(4) + 2(8) = 8 + 16 = 24
Among these options, the pair (4,8) yields the smallest perimeter, which is 24.
Therefore, the least perimeter of a rectangle with an area of 32 square feet is 24 feet.