If I know the SquareFeet (Sq.Ft.) of a plot, can I calculate Length (L) and Width (W)

Question

If I have a Square Feet (Sq. Ft.) of 28314, how can I calculate one possible Length (L) and Width (W) assuming it is a rectangle? I realize there are different possibilities/combinations of L& W, but the method of arriving at one such possibility would suffice.

Answer 1

How do you calculate the area of a rectangle?

 

Write an equation.

 

Substitute what you know into your equation. ...

 

Area = Length times Width

 

A = LW

 

28314 = LW

 

Substitute any real number for either L or W and solve for the other. That will give you values for both L and W.

 

E.g., L = pi,

 

28314 = (pi)W

 

W = 28314/pi ≈ 9012.62611740784976

Answer 2

If you want whole number answers vice real numbers, you have to factor the number 28314 until you get to prime numbers.

• 1 x 28314 in an answer
• 1 is a prime number but 28314 is an even number, it is divisible by 2, so 2 x 14157 = 28314
• 2 is a prime number but 14517 is divisible by 3, so 1 x 2 x 3 x 4719 = 28134
• 3 is also a prime number but 4719 is also divisible by 3, so 1 x 2 x 3 x 3 x 1573 = 28134
• 1573 is divisible by 11, so 1 x 2 x 3 x 3x 11 x 143 = 28314
• Finally 143 is divisible by 11, so we're down to the prime factors 1 x 2 x 3 x 3 x 11 x 11 x 13

Any combination of these works, such as (1x 2 x 3 x 3 x 11) x (11 x 13) = (198) x (143) = 28314 or (1 x 2 x 3 x 3) x (11 x 11 x 13) = (18) x (1573) = 28314.

 

Answer 3

Write the prime factorization of 28314.

28314/2=14157

14157/3=4719

4719/3=1573

1573/11=143

143/11=13

28314=2*3*3*11*11*13

Using these factors, make a width and a length.

For example, 198*143=28314