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Ksenya-84 [330]
2 years ago
12

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

Mathematics
1 answer:
soldi70 [24.7K]2 years ago
5 0

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}

Visit: brainly.com/question/10452031

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