A rectangular garden is 20 ft longer than it is wide. Its area is 8000 ft{}^2. What are its dimensions?
w(w+20) = 8000
w^2+20w = 8000
w^2+20w-8000 = 0
(w-80)(w+100) = 0
w-80 = 0
w=80
or
w+100 = 0
w = -100
I think that x=80 makes more sense. However what would the length be if the width is equal to 80 in this problem ? please help Im stuck and am not sure what the final answer for this question would be.
Excuse me? You already know that the length is 20 more than the width.
So, if the width is 80, the length is 100.
Sure enough, 80*100 = 8000
Or, since you know the width is 80, and area = length*width
8000 = 80 * length
length=100
Don't forget your algebra I now that you're taking college algebra.
Thank You. I guess I was over thinking the problem a bit!lol It's my first semester and everything's so new.
Thanks so much again
If the width is 80 ft, as you have determined, then the length would be 80 + 20 = 100 ft (since the length is 20 ft longer than the width). So, the dimensions of the rectangular garden would be 80 ft by 100 ft.
If the width of the garden is 80 ft, as determined by solving the quadratic equation w^2 + 20w - 8000 = 0, we can calculate the length by plugging this value back into the given equation.
The length of the garden is given by w + 20, so when w = 80,
Length = 80 + 20 = 100 ft.
Therefore, if the width of the garden is 80 ft, the length would be 100 ft.
To find the length, you can use the given information that the width is 80 ft.
Since the length of the rectangular garden is 20 ft longer than its width, you can calculate the length by adding 20 ft to the width.
Length = Width + 20
Length = 80 + 20
Length = 100
Therefore, the dimensions of the rectangular garden are 80 ft by 100 ft.