word problems in algebra

Question

If Sally wants to create a vegetable garden in her backyard.  She wants to have the area of 120 sq ft., and it will be 12ft longer than it is wide. What should she use for the vegetables garden.  rouund to nearest 100th foot

Answer 1

We'll use the equation Area = length × width to solve this problem. For your problem, A = 120. Let's let width = x. That would make length x + 12, since the garden is 12 feet longer than it is wide. Now just plug those values in:

 

120 = (x+12)x

120 = x² + 12x

 

Rearrange the equation to look like a quadratic and use the Quadratic Formula for a = 1, b = 12, and c = -120:

 

0 = x² + 12x - 120

 

x = (-12 ± √(12² - 4(1)(-120))) / 2(1)

x = (-12 ± √(144 + 480)) / 2

x = (-12 ± √624) / 2

x = (-12 ± 24.98) / 2

 

x = (-12 + 24.98) / 2    OR    x = (-12 - 24.98) / 2

x = 6.49    OR    x = -18.49

 

Since width can't be negative, the garden must be x = 6.49 feet wide and x+12 = 6.49+12 = 18.49 feet long.