The length of a rectangle is 4 feet shorter than its width. the area of the rectangle is 42 square feet. find the length and width. round your answer to the nearest tenth of a foot

Length is feets and width is equal to feets.

Area of a rectangle

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.

A quadrilateral having four right angles is known as a rectangle.

Let feets denotes width of a rectangle.

Length of a rectangle feets

Area of a rectangle square feet

Length Width

     

   

As dimension can not be negative, is rejected.

So,

    feets

Length

            feets

So, length is feets and width is equal to feets.

Find out more information about rectangle here:

link

Let the length of the rectangle to be a value, x.

Since you are told that the length is 4 feet shorter than width, then, this can only mean that 
width = (x+4)
The area of a rectangle = length × width. 
                                      = x(x+4) = 42
                                      =x² + 4x=42
 From here form the quadratic equation then solve it to get the value of x (length of the rectangle)

x²+4x-42=0
Using the quadratic formula,

x = -4 + or - (√(16-4×1×-42))÷2

At this point I had a problem with inserting an equation in this platform. So, i have done it have attached a file that explains the above statement. Kindly find it in the attachment below.  

x = (-4+or - 13.56)÷2
  = 9.56÷2
  =4.78 feet
The length to the nearest foot = 5 feet.
The width to the nearest foot = 5+4 = 9 feet.