THe width of a garden is 8 feet less than the length. If the area of the garden is 20 square feet, find the length and the width.
could someone work this for me. I have but not right.
What if the length is 10 feet?
LW=20
W=L-8
L(L-8)=20
L^2-8L-20=0
(L-10) (L+2)
Only 10 works. When we put ten back in either, equation you get 2 for W.
Sure! I can help you solve this problem. To find the length and width of the garden, we can set up an equation using the given information.
Let's assume that the length of the garden is 'x' feet.
According to the given information, the width of the garden is 8 feet less than the length. So, the width can be represented as (x - 8) feet.
The area of a rectangle is equal to its length multiplied by its width. In this case, the area of the garden is given as 20 square feet. So, we can set up the equation:
Length * Width = Area
x * (x - 8) = 20
Now, we can solve this equation to find the length and width of the garden.
Expanding the equation, we get:
x^2 - 8x = 20
Rearranging the equation and subtracting 20 from both sides, we get:
x^2 - 8x - 20 = 0
To solve this quadratic equation, there are multiple methods like factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -8, and c = -20.
Substituting these values into the quadratic formula, we get:
x = (8 ± √((-8)^2 - 4 * 1 * (-20))) / 2*1
x = (8 ± √(64 + 80)) / 2
x = (8 ± √144) / 2
Simplifying further, we get:
x = (8 ± 12) / 2
Now, we have two possible solutions:
1) x = (8 + 12) / 2 = 20 / 2 = 10
2) x = (8 - 12) / 2 = -4 / 2 = -2
Since the length of the garden cannot be negative, we disregard the second solution.
So, the length of the garden is 10 feet.
To find the width, we can substitute the value of x into the width expression (x - 8):
Width = Length - 8 = 10 - 8 = 2
Therefore, the length of the garden is 10 feet, and the width is 2 feet.