A rectangular piece of sheet metal is 4 ft longer than it is wide. (See the illustration.) The area of the piece of sheet metal is 96 ft2. Find its length and width

A = lw

96 = (w+4)(w)

w^2 + 4w -96 = 0

(w +12 )(w-8) =0

w=-12 cannot have a neg value here

w = 8

so l = 12

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

A rectangular piece of sheet metal is 4 ft longer than it is wide .(See 2

Illustration below ). The area of the piece of sheet is 21 ft . Find its length and width. (Hint : Area of the rectangle = Length ×Width )

To find the length and width of the rectangular piece of sheet metal, we can use the given information about the area and the relationship between the length and width.

Let's assume the width of the sheet metal is "w" feet.

According to the problem, the length of the sheet metal is 4 ft longer than the width. So, the length would be "w + 4" feet.

The area of a rectangle can be found by multiplying its length and width. We know that the area is given as 96 ft². Therefore, we can set up the following equation:

Area = Length * Width

96 = (w + 4) * w

Now, we can solve this quadratic equation to find the values of "w" and "w + 4" that satisfy the equation.

First, we can expand the equation:

96 = w^2 + 4w

Rearranging the equation:

w^2 + 4w - 96 = 0

Now, we can solve this equation for "w" using factoring, completing the square, or quadratic formula.

By factoring, we can find that the equation factors as:

(w + 12)(w - 8) = 0

So, either w + 12 = 0 or w - 8 = 0.

Solving for "w" in each equation:

1. w + 12 = 0
w = -12

2. w - 8 = 0
w = 8

Since the width cannot be negative, we ignore the first solution (w = -12).

Therefore, the width of the rectangular piece of sheet metal is 8 ft.

To find the length, we can substitute the value of "w" into the expression for the length:

Length = Width + 4
Length = 8 + 4
Length = 12

Hence, the length of the rectangular piece of sheet metal is 12 ft, and the width is 8 ft.