Question

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft2. What is the dimension of the parking lot?

Answer 1

`L = 210`,
`W=200`

`W=210`,
`L = 200`

Explanation:

By definition, the perimeter of a rectangle is:

`P = 2L + 2W`

Where:

P is the perimeter, L is the length and W is the width

Also, the area of a rectangle is:

`A = LW`

Where L is the length of the base and W is the width.

We know that for this rectangle:

`P = 2L + 2W = 820 ft\\\\A = LW = 42,000 ft ^ 2`

Now we have two equations and two unknowns (L and W)

Then we solve the system.

`L = (42,000)/(W)`

Now we substitute this relation in the perimeter equation.

`2((42,000)/(W)) + 2W = 820\\\\(42,000)/(W) + W = 410\\\\42000 + W ^ 2 = 410W\\\\W ^ 2 -410W + 42000 = 0\\\\(W - 210)(W - 200) = 0\\\\W = 210\\\\W = 200`

Then for W=210:

`L = (42000)/(W)\\\\L = (42000)/(210)\\\\L = 200`

And for W=200

`L = (42000)/(200)\\\\L = 210`

Answer 2

`210 \: by \: 200`

EXPLANATION

Let l and w be the dimensions of the parking lot

The perimeter of the parking lot is given by

`p =2( l + w)`

This implies that

`820 = 2(l + w)`

Dividing both sides by 2

`l + w = (820)/(2)`

`l + w = 410......eq1`

Area of the of the parking lot is given by

`l * w = 42000...........eqn2`

putting eqn 1 into ran 2

`410l - {l}^(2) = 42000`

`0= {l}^(2) - 410l + 42000`

`{l}^(2) - 210l - 200l+ 42000 = 0`

`( {l}^(2) - 210l )-1( 200l - 42000 )= 0`

`l ( {l} - 210l )- 200(l - 210)= 0`

`( {l} - 210l )(l - 200)= 0`

`l = 210 \: or \: 200`

if

`l = 200`

then

`w = 210`

and also if

`l = 210`

then

`w = 200`

Hence the dimensions of the parking lot is

`210 \: by \: 200`