The length and width of the rectangular wall of a barn having an area of 120 square feet, and having a length 8 more than twice its width are 20 feet and 6 feet respectively.
What is the area of a surface?
The amount of space covered by a cross-section in two dimensions is the area of that surface.
What is the area of a rectangle?
The area of a rectangle is the product of its length and width.
The area of the rectangle = Length * Width
How to solve the given question?
In the question, we are given a rectangular wall of a barn having an area of 120 square feet. The length of the wall is 8 feet longer than twice its width.
We are asked to find the length and width of the wall of the barn.
We assume the width of the wall as x feet.
Therefore, the length of the wall = 8 feet longer than twice its width= 8 + 2x feet.
Now, the area of the wall = length * width,
or, 120 = (8 + 2x)x
or, 120 = 8x + 2x²
or, 2x² + 8x - 120 = 0
or, x² + 4x - 60 = 0
or, x² + 10x - 6x - 60 = 0
or, x(x + 10) - 6(x + 10) = 0
or, (x - 6)(x + 10) = 0
By zero-product law, we know that:
Either, x - 6 = 0 ⇒ x = 6.
or, x + 10 = 0 ⇒ x = -10.
Since x is the width of the wall, it can not be negative. Thus we take x = 6.
∴ Width of the wall of the barn = 6 feet
Length of the wall of the barn = 8 + 2*6 = 8 + 12 = 20 feet.
∴ The length and width of the rectangular wall of a barn having an area of 120 square feet, and having a length 8 more than twice its width are 20 feet and 6 feet respectively.
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