Answer :
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*
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:
Dimensions of the garden are 24 feet by 8.33 feet.
Step-by-step 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 = [tex]\frac{1\pm \sqrt{1^{2}+2400}}{6}[/tex]
= [tex]\frac{1\pm \sqrt{2401}}{6}[/tex]
= [tex]\frac{1\pm 49}{6}[/tex]
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
