The expressions for the width, W, and area, A, of the rectangle in terms of L are:
- W =
- L - A =
![\frac{13L - L^{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13L%20-%20L%5E%7B2%7D%20%7D%7B2%7D)
The expression for the perimeter of a rectangle is given as:
P = 2(L + W)
where L is its length and W its width
a. Given that the perimeter of the rectangle is 13 feet, then;
13 = 2(L + W)
divide through by 2
= L + W
So that;
W =
- L
The required formula for the width as a function of L is: W =
- L
b. Area of a rectangle can be expressed as;
A = L * W
substitute the expression for width in that of area to have
A = L * (
- L)
=
L - ![L^{2}](https://tex.z-dn.net/?f=L%5E%7B2%7D)
A = ![\frac{13L - L^{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13L%20-%20L%5E%7B2%7D%20%7D%7B2%7D)
The expression for the area A is: A = ![\frac{13L - L^{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13L%20-%20L%5E%7B2%7D%20%7D%7B2%7D)
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