Question

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 work.

Answer 1

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*

Answer 2

Dimensions of the garden are 24 feet by 8.33 feet.

Explanation:

Let the dimensions of the vegetable garden is length = l and width = w foot

Area of the vegetable garden = 200 square feet

Since length of the garden is 1 foot less than the 3 times the width.

l = 3w - 1

Area of the garden = w × l = 200

w(3w - 1) = 200

3w² - w = 200

3w² - w - 200 = 0

By quadratic formula

w =
`\frac{1\pm \sqrt{1^(2)+2400}}{6}`

=
`(1\pm √(2401))/(6)`

=
`(1\pm 49)/(6)`

w = -8 or 8.33 foot

Since dimensions can not be negative therefore, width of the garden will be 8.33 foot

Since l = 3w - 1

= 3×8.33 - 1

= 25 - 1

= 24

Dimensions of the garden are 24 feet by 8.33 feet