Jeremy has 50 ft of fencing to enclose a rectangular-pen for his dog. He plans on using a side of his house for one side of the

Question

1 year ago

5

pen. What dimensions will produce an enclosed area of 288 ft?

1 answer:

kotykmax [81] · Answer 1 · 2024-06-13T18:07:39+03:00

The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.

<h3>What is the dimension of length and width?</h3>

We know that,

P = l + 2w

50 = l + 2w

50 - 2w = l

A = l x w

288 = (50 - 2w)w

288 = 50w -2w²

2w² - 50w + 288

By dividing throughout by 2

w² - 25w + 144

This is in quadratic equation form.

By applying quadratic formula,

w = (-(-25) ± $\sqrt{(-25)^{2}-4*1*144$ ) / 2

w = (-(-25) ± 7)/2

w1 = (-(-25) + 7)/2

w1 = (25 + 7) / 2

w1 = 16

w2 = (-(-25) - 7)/2

w2 = (25 - 7) / 2

w2 = 9

By substituting the values in eq1,

A = l x w

if w = 16

288 = l x 16

l = 288/16

l = 18

if w = 9

288 = l x 9

l = 288/9

l = 32

The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.

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