A rectangular piece of sheet metal is 4 ft longer than it is wide. The area of the piece of sheet metal is 45 ft2. Find its length and width.

length = width + 4

length + width = 45
ok whatever the answer is 9 and 5

Let's assume the width of the rectangular piece of sheet metal is "x" feet.

According to the information given, the length of the sheet metal is "4 ft longer" than its width. So, the length of the sheet metal is x + 4 feet.

To find the area of the sheet metal, we multiply its length and width. Given that the area is 45 square feet, we can set up the following equation:

(x + 4) * x = 45

Expanding the equation:

x^2 + 4x = 45

Rearranging the equation to form a quadratic equation:

x^2 + 4x - 45 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:

(x + 9)(x - 5) = 0

Setting each factor to zero:

x + 9 = 0 or x - 5 = 0

Solving the first equation:

x = -9

Solving the second equation:

x = 5

Since a negative length doesn't make sense in this context, we discard the -9 as a non-viable solution.

Therefore, the width of the rectangular piece of sheet metal is 5 feet, and the length is 5 + 4 = 9 feet.

To find the length and width of the rectangular piece of sheet metal, we can set up an equation based on the given information.

Let's assume that the width of the sheet metal is x ft.

According to the given information, the length of the sheet metal is 4 ft longer than its width. So, the length can be represented as (x + 4) ft.

The area of a rectangle is given by the formula:

Area = Length * Width

In this case, the area is given as 45 ft². So, we can write the equation as:

45 = (x + 4) * x

Now, let's solve this equation to find the value of x and then determine the length and width.

Expanding the equation:

45 = x^2 + 4x

Rearranging the equation:

x^2 + 4x - 45 = 0

Now, we can solve this quadratic equation for x by factoring, completing the square, or using the quadratic formula:

Since this equation can be factored easily, let's factor it:

(x + 9)(x - 5) = 0

Setting each factor equal to zero:

x + 9 = 0 or x - 5 = 0

Solving for x in each equation:

x = -9 or x = 5

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the sheet metal is 5 ft.

Now, to find the length, we substitute the value of x into either equation:

Length = x + 4 = 5 + 4 = 9 ft

So, the length of the rectangular sheet metal is 9 ft and the width is 5 ft.