SOLUTION: A small rectangular vineyard is to have an overall dimension of 100 feet by 200 feet. Surrounding the vineyard there will be a grassy border of uniform width. The total area of the

Algebra ->  Surface-area -> SOLUTION: A small rectangular vineyard is to have an overall dimension of 100 feet by 200 feet. Surrounding the vineyard there will be a grassy border of uniform width. The total area of the      Log On


   

Question 795458: A small rectangular vineyard is to have an overall dimension of 100 feet by 200 feet. Surrounding the vineyard there will be a grassy border of uniform width. The total area of the vineyard and the grassy area is 21525 square feet.
Write an equation for total area in terms of the width of the grassy area x:
A(x)=
If the total area is 21525 square feet, determine the width of the grassy area. The width of the grassy area is ________ feet.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Area of just the vineyard, 100%2A200=20000 ft%5E2.

Area of the grassy border AND vineyard combined, %282x%2B100%29%282x%2B200%29=21525

Algebra steps:
4x%5E2%2B400x%2B200x%2B20000=21525
4x%5E2%2B600x=1525
highlight%284x%5E2%2B600x-1525=0%29

Use the general solution to quadratic formula to solve for x, unless you can find a way to factor the quadratic expression.

x=%28-600%2Bsqrt%28600%5E2-4%2A4%28-1525%29%29%29%2F%282%2A4%29
x=%28-600%2Bsqrt%28360000%2B16%2A1525%29%29%2F8
x=%28-600%2Bsqrt%28384400%29%29%2F8
x=%28-600%2B620%29%2F8
x=20%2F8=10%2F4=5%2F2
highlight%28x=2%261%2F2%29 feet.