MHB Find Area Formula of Rectangle

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To find the area of a rectangle with a perimeter of 30 feet, the width is denoted as x. The perimeter formula, P = 2L + 2W, leads to the equation 30 = 2L + 2x, allowing for the calculation of length as L = (30 - 2x)/2. The area formula A = LW can then be expressed as A = x(15 - x) after substituting for L. This confirms that the length and width of the rectangle sum to half the perimeter.
mathdad
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Let x denote the width of a rectangle with perimeter 30 feet. Find the area of this rectangle.

Let me see.

P = 2L + 2W

30 = 2L + 2x

(30 - 2x) = 2L

(30 - 2x)/2 = L

A = LW

A = [(30 - 2x)/2]x

Correct?

I guess we can simplify a little more.

A = x(15 - x)

Correct?
 
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yes ... the length & width of a rectangle sum to half the perimeter

$P = 2(L+W) \implies L+W = \dfrac{P}{2}$
 
Good to be right.
 
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