The parking lot is 25 by 40 feet. The owner wants to enlage the parking lot by paving an equal width strip on the north side and east side of the lot, sot hat the new lot will be twice the area of the old one. Find the equation which has as a root the proper width of the strip.
let the width of the strip to be added be x ft
new length = x+40
new width = x+25
new area = (x+40)(x+25)
old area = 25x40 = 1000
(x+40)(x+25) = 2000
x^2 + 65x - 1000 = 0
All you asked for was the equation,
solve it using the quadratic equation formula
Got it thanks. I had gotten up to the equation but completely forgot to plug it into the quadratic to get my answer of 12.845
Thanks again.
To solve this problem and find the equation with the proper width of the strip as a root, let's break it down step by step:
1. Determine the dimensions of the old parking lot:
- Given: Length = 25 feet and Width = 40 feet
2. Calculate the area of the old parking lot:
- Old Area = Length * Width = 25 feet * 40 feet = 1000 square feet
3. Determine the desired area of the new parking lot:
- New Area = 2 * Old Area = 2 * 1000 square feet = 2000 square feet
4. Enlarge the parking lot by adding a strip on the north and east sides:
- Let's assume the width of the strip is "w" feet.
- The new length will be increased by "w" feet: Length + w
- The new width will be increased by "w" feet: Width + w
5. Calculate the new area of the parking lot after enlargement:
- New Area = (Length + w) * (Width + w)
6. Set up the equation using the desired area:
- New Area = 2000 square feet
- (Length + w) * (Width + w) = 2000
7. Expand and simplify the equation:
- Length * Width + Length * w + Width * w + w^2 = 2000
- 1000 + 25w + 40w + w^2 = 2000
- w^2 + 65w - 1000 = 0
8. Finally, the equation that has the proper width of the strip as a root is:
- w^2 + 65w - 1000 = 0
By solving this quadratic equation, you can find the proper width of the strip that will fulfill the condition of doubling the area of the parking lot.