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Sati [7]
2 years ago
10

Tina is planning to fence in an area for her dog. She wants to create a rectangular area of 1,600 square feet for her pet and ca

n afford to purchase 160 feet of fence. In two or more complete sentences, explain the algebraic model, calculations and reasoning necessary to determine the dimensions of the rectangular area.
Mathematics
1 answer:
castortr0y [4]2 years ago
4 0

The dimensions of the rectangular area of Tina's fence is 40 ft by 40 ft

<h3 />

<h3>Area of a rectangle:</h3>
  • area = lw

where

l = length

w = width

She wants to create a rectangular area of 1,600 square feet for her pet . Therefore,

  • area = 1600 ft²

lw = 1600

Therefore,

perimeter = 160 ft

Then,

perimeter of rectangle = 2(l + w)

160 = 2(l + w)

l + w = 80

Let's combine the equations

lw = 1600

l + w = 80

l = 80 - w

Therefore,

w(80 - w) = 1600

80w - w² = 1600

Therefore,

w² - 80w + 1600 = 0

w² - 40w - 40w + 1600 = 0

w(w - 40) - 40(w - 40) = 0

(w - 40)(w - 40) = 0

w = 40 or 40

Therefore, the dimensions can be calculated as follows:

lw = 1600

40l = 1600

l = 1600 / 40

l = 40 ft

Therefore, the dimensions are 40ft by 40 ft

learn more on algebraic model here: brainly.com/question/4151078

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