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Let us take a rectangle with length L and width W. The perimeter of the rectangle is P = 2W + 2L
W = (P - 2L)/2
The area of the rectangle is W*L = L*(P - 2L)/2
In terms of length L and the perimeter P the area of a rectangle is L*(P - 2L)/2
We know that the area of a rectangle is the product of the length and the width.
A = L*w
The perimeter of rectangle is:
P = 2(L + w)
Since the area has to be expressed only in terms of perimeter and length, we'll express the width in terms of P and L.
P = 2L + 2w
2w = P - 2L
w = (P-2L)/2
A = [L*(P-2L)]/2
Therefore the area of a rectangle, expressed only in terms of perimeter and length, is A = [L*(P-2L)]/2.
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