The length of a rectangle is 4 ft. longer than its width w. the area of the floor is 525 ft^2. 1) draw a picture of the situation. 2) write a quadratic equation for the area in terms of w that represents the situation. 3) what are the dimensions of the floor?

For this case the first thing you should know is that the area of the rectangle is given by:
 A = (w) * (l)
 Where,
 w: width
 l: length
 Substituting values we have:
 A = (w) * (w + 4)
 Rewriting we have:
 A (w) = w ^ 2 + 4w
 Then, the dimensions will be:
 525 = w ^ 2 + 4w
 w ^ 2 + 4w - 525 = 0
 Which roots are:
 w = -25
 w = 21
 We ignore the negative root, the dimensions are:
 w = 21 feet
 l = w + 4 = 21 + 4 = 25 feet
 
 a quadratic equation for the area in terms of w that represents the situation is:
 A (w) = w ^ 2 + 4w
 the dimensions of the floor are:
 w = 21 feet
 l = 25 feet