How to express the area of rectangle in terms of perimeter and length?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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