40 = l * w l = w + 6
substitute (w + 6) in for l
40 = (w+6)*w 40 = w^2 + 6w 0 = w^2 + 6w - 40 0 = (w + 10) * (w - 4)
w + 10 = 0 w = -10
w - 4 = 0 w = 4
it does not make sense for the width to be negative, so 4 is the correct answer now go back to one of the original equations, l = w + 6
l = w + 6 l = 4 + 6 l = 10
The **width **of the **wall **is 4 feet and the **length **of the wall is 10 feet.
What is Algebra?
**Algebra **is a branch of mathematics that **deals with mathematical operations and relations using letters **and **symbols **to represent numbers and quantities. It involves solving equations and finding patterns and relationships between variables.
Let's denote the width of the wall as x.
Then, length= x +6
The **area **of a **rectangle **is calculated as length times width, so we can set up an equation:
x(x + 6) = 40
x² + 6x = 40
x² + 6x - 40 = 0
Now we can solve this **quadratic equation **by factoring or using the quadratic formula.
(x + 10)(x - 4) = 0
x + 10 = 0 or x - 4 = 0
x = -10 or x = 4
Since the width of the wall cannot be negative, we discard the solution x = -10.
Therefore, the **width **of the **wall **is x = 4 feet.
Length = x + 6 = 4 + 6 = 10 feet
So the **width **of the **wall **is 4 feet and the **length **of the wall is 10 feet.
Learn more about Algebra here:
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The width of the wall is 4 feet, and the length is 10 feet. This is found by setting up a system of equations based on the area and the relationship between length and width. By solving the quadratic equation, we determined the dimensions of the barn wall.
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