Question

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?

Answer 1

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