among all rectangles that have a perimeter of 48 Then the dimensions of the one whose area is largest is 12 by 12
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 48
2L + 2W = 48
L + W = 24
W = 24 - L
The area of the rectangle is expressed as:
A = LW
A = L(24-L)
A = 24L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 24 - 2L
0 = 24 - 2L
2L = 24
L = 24/2
L = 12
Recall that 2(L+W) = 48
2(12 + W) = 48
12 + W = 24
W = 24 - 12
W = 12
Hence the dimensions of the one whose area is largest is 12 by 12
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