Question

The 13-foot string is arranged into a rectangle. Let L denote the length of the rectangle,

Answer 1

The expressions for the width, W, and area, A, of the rectangle in terms of L are:

• W = $\frac{13}{2}$ - L
• A = $\frac{13L - L^{2} }{2}$

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

$\frac{13}{2}$ = L + W

So that;

W = $\frac{13}{2}$ - L

The required formula for the width as a function of L is: W = $\frac{13}{2}$ - 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 * ( $\frac{13}{2}$ - L)

  = $\frac{13}{2}$L - $L^{2}$

A = $\frac{13L - L^{2} }{2}$

The expression for the area A is: A = $\frac{13L - L^{2} }{2}$

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