A vegetable garden with an area of 200 square feet is to be fertilized. If the length of the garden is 1 foot less than three times the width, find the dimensions of the garden.

Please show your work.

Ok so I like to go in steps with these questions- first draw a picture and identify your variables.
W=width L= 3w-1
Now we know that length times width gets us area so we plug in our variables into the area equation.
200 = w(3w-1)
When you foil that equation you end up with a quadratic : 3w^2-w-200 = 0
Either factor that or use the quadratic formula to get w= 8.33 and w= -8
Since you can't have a negative dimension you need to use 8.33 and plug it back into your length equation.
Final answer:
w= 8.33ft l= 23.99ft
Now I simplified the decimals a little bit so you end up with 199.8ft^2 for the area so just add a few decimals on here and there

Answered by ottln1 | 2024-06-10

Dimensions of the garden are 24 feet by 8.33 feet. ;

Answered by eudora | 2024-06-12

The dimensions of the vegetable garden are approximately 24 feet in length and 8.33 feet in width. The width was determined to be approximately 8.33 feet using the quadratic formula, and the corresponding length calculated as 24 feet. This fits the criteria of an area of 200 square feet while satisfying the given relationship between length and width.
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Answered by eudora | 2024-12-26