The length of a certain lot if 20 feet less than four times its width. the area of 4200 sq. ft. what are the dimensions of the lot?

The area of a surface is the number of square units present in the surface. For a rectangle, it is calculated from the product of the length and the width. To determine the length and width of the lot given above, we first assume that it is in a rectangular shape which is defined by its length and its width. We are given the following:

Area = 4200 square feet

Length = 4x - 20 feet

Width = x feet

From the definition of the area of a rectangle,

Area = length x width

4200 = (4x - 20) (x)

4200 = 4x^2 - 20x

4x^2 - 20x - 4200 = 0

4 (x^2 - 5x - 1050) = 0

x^2 - 5x - 1050 = 0

Factoring the equation would lead to:

(x - 35) (x + 30) = 0

x - 35 = 0; x = 35

x + 30 = 0; x = - 30

The width should not be a negative value so the width would be equal to 35 feet. So, the length would be

Length = 4 (35) - 20 = 120 feet