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 set up an equation using the given information.

Let's assume the width of the sheet metal is 'x' feet. Since the length is 4 feet longer than the width, we can express the length as (x+4) feet.

The formula for the area of a rectangle is length times width, so we can set up the equation:

x(x+4) = 12 ft²

Expanding the equation gives us:

x² + 4x = 12 ft²

Rearranging the equation by subtracting 12 ft² from both sides, we get:

x² + 4x - 12 = 0

Now, we can solve this quadratic equation by factoring.

We look for two numbers that multiply to give -12 and add up to 4. The numbers that satisfy this condition are -2 and 6.

So, we can rewrite the equation as:

(x - 2)(x + 6) = 0

Now we set each factor equal to zero and solve for x:

x - 2 = 0 or x + 6 = 0

Solving each equation gives us:

x = 2 or x = -6

Since the width cannot be negative, we discard the solution x = -6.

Therefore, the width of the rectangular piece of sheet metal is 2 ft.

To find the length, we substitute the value of x into the expression for length: length = x + 4.

length = 2 + 4 = 6 ft

So, the length of the rectangular piece of sheet metal is 6 ft and the width is 2 ft.