The area of a 300' by 400' rectangle is doubled by adding a strip of width around the perimeter. Approximately how wide is that strip?

old area = 300*400 = 120 000

new area = 240 000

(300+2x)(400+2x) = 240000
120000+1400x + 4x^2 = 240000
simplify and divide by 4.

x^2 + 350x - 30000 = 0
x = (-350 ± √242500)/2
= appr 71.22 or some negative which we will reject

To solve this problem, we need to find the width of the strip that is added to the perimeter of the rectangle.

First, let's calculate the area of the original rectangle without the strip. The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 300 feet and the width is 400 feet.

Original area = Length * Width
Original area = 300 feet * 400 feet
Original area = 120,000 square feet

Now, let's find the area of the enlarged rectangle after the strip is added. The enlarged rectangle has twice the area of the original rectangle.

Enlarged area = 2 * Original area
Enlarged area = 2 * 120,000 square feet
Enlarged area = 240,000 square feet

The strip is added around the perimeter, which means it contributes to both the length and width. Let's assume the width of the strip is x feet. Therefore, the new length and width of the enlarged rectangle would be:

New length = Length + 2 * x
New width = Width + 2 * x

The area of the enlarged rectangle can also be calculated using these new length and width:

Enlarged area = New length * New width
240,000 square feet = (300 feet + 2x) * (400 feet + 2x)

Now, we have a quadratic equation. We can expand and solve it to find the value of x, which will give us the width of the strip.

240,000 square feet = (300 feet + 2x) * (400 feet + 2x)
240,000 square feet = 120,000 square feet + 600 feet * x + 800 feet * x + 4x^2
240,000 square feet = 120,000 square feet + 1,400 feet * x + 4x^2

Rearranging the equation:

4x^2 + 1,400 feet * x + 120,000 square feet - 240,000 square feet = 0
4x^2 + 1,400 feet * x - 120,000 square feet = 0

Next, we can solve this quadratic equation using methods like factoring, completing the square, or the quadratic formula.

By solving this quadratic equation, you can find the value of x, which will give you the approximate width of the strip.