A rectangular piece of sheet metal is 4 ft longer than it is wide. (See the illustration in the link below.) The area of the piece of sheet metal is 12 ft^2. Find its length and width.
www.webassign.net/ewenmath10/11-3-003-alt.gif
length =x+4
width =x
x(x+4)=12
x^2+4x-12=0
x^2-2x+6x-12=0
x(x-2)+6(x-2)=0
(x+6)(x-2)=0
length = 6
width = 2
To find the length and width of the rectangular piece of sheet metal, we can use the given information about its dimensions and area.
Let's assume the width of the sheet metal to be x ft.
According to the problem, the length of the sheet metal is 4 ft longer than its width. So, the length is (x + 4) ft.
The formula for the area of a rectangle is: area = length * width.
Given that the area of the sheet metal is 12 ft², we can write the equation:
12 = (x + 4) * x
To solve this quadratic equation, we can proceed as follows:
Expanding the equation:
12 = x² + 4x
Rearranging the equation to set it equal to zero:
x² + 4x - 12 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Factoring this equation, we can write it as:
(x + 6)(x - 2) = 0
Setting each factor equal to zero and solving for x:
x + 6 = 0 or x - 2 = 0
For x + 6 = 0, x = -6. Since the width cannot be negative, we disregard this solution.
For x - 2 = 0, x = 2.
Therefore, the width is 2 ft.
We can find the length by substituting the width value into the equation for the length:
length = x + 4 = 2 + 4 = 6 ft.
Hence, the length of the rectangular piece of sheet metal is 6 ft and the width is 2 ft.
To find the length and width of the rectangular piece of sheet metal, we can set up an equation using the given information.
Let's assume the width of the sheet metal is "x" ft. According to the problem, the length of the sheet metal is 4 ft longer than its width, so the length can be represented as "x + 4" ft.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 12 ft^2.
So we can write the equation:
Length * Width = Area
(x + 4) * x = 12
Now, we can solve this equation to find the values of x and x + 4.
Expanding the equation further:
x^2 + 4x = 12
Rearranging the equation into standard quadratic form:
x^2 + 4x - 12 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 4, and c = -12.
Plugging the values into the quadratic formula:
x = (-4 ± √(4^2 - 4 * 1 * -12)) / (2 * 1)
Simplifying:
x = (-4 ± √(16 + 48)) / 2
x = (-4 ± √64) / 2
x = (-4 ± 8) / 2
We have two possible solutions:
1. x = (-4 + 8) / 2 = 4 / 2 = 2
2. x = (-4 - 8) / 2 = -12 / 2 = -6
Since the width of the sheet metal cannot be negative, we discard the second solution.
Therefore, the width of the sheet metal is 2 ft.
To find the length, we can substitute the value of x back into the equation:
Length = x + 4 = 2 + 4 = 6 ft
So, the length of the sheet metal is 6 ft and the width is 2 ft.