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A rectangular parking lot must have a perimeter of 440 feet and an area of at least 8000 square feet. Describe the possible lengths of the parking lot.

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Answer:

The possible parking lengths are 45.96 feet and 174.031 feet

Step-by-step explanation:

Let x be the length of rectangular plot and y be the breadth of rectangular plot

A rectangular parking lot must have a perimeter of 440 feet

Perimeter of rectangular plot =2(l+b)=2(x+y)=440

2(x+y)=440

x+y=220

y=220-x

We are also given that an area of at least 8000 square feet.

So, [tex]xy \leq 8000[/tex]

So,[tex]x(220-x) \leq 8000[/tex]

[tex]220x-x^2 \leq 8000[/tex]

So,[tex]220x-x^2 = 8000\\-x^2+220x-8000=0[/tex]

General quadratic equation : [tex]ax^2+bx+c=0[/tex]

Formula : [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-220 \pm \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=\frac{-220 + \sqrt{220^2-4(-1)(-8000)}}{2(-1)} , \frac{-220 - \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=45.96,174.031[/tex]

So, The possible parking lengths are 45.96 feet and 174.031 feet

MrRoyal

The perimeter of a shape is the sum of its side lengths

The possible dimension of the parking lot is 46ft by 174ft

Let the dimension of the rectangular parking lot be x and y.

So, we have:

[tex]\mathbf{P = 2(x + y) = 440}[/tex] -- perimeter

[tex]\mathbf{A = xy = 8000}[/tex] --- area

Divide both sides of the perimeter equation by 2

[tex]\mathbf{x+y =220}[/tex]

Make x the subject

[tex]\mathbf{x =220 - y}[/tex]

Substitute [tex]\mathbf{x =220 - y}[/tex] in [tex]\mathbf{A = xy = 8000}[/tex]

[tex]\mathbf{(220 - y)y = 8000}[/tex]

Open brackets

[tex]\mathbf{220y - y^2 = 8000}[/tex]

Rewrite as:

[tex]\mathbf{y^2 -220y + 8000 = 0}[/tex]

Using a calculator, the possible values of y are:

[tex]\mathbf{y = 174\ or\ y = 46}[/tex]

Recall that:

[tex]\mathbf{x =220 - y}[/tex]

So, we have:

[tex]\mathbf{x = 220 - 174\ or\ x = 220 -46}[/tex]

[tex]\mathbf{x = 46\ or\ x = 174}[/tex]

Hence, the possible dimension of the parking lot is 46ft by 174ft

Read more about perimeters and areas at:

https://brainly.com/question/16103242

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