Calc

What Size Is It

Question asked by alan johnston:

building is square, it is 20,000 square ft, what is the length of any one side.12160

Follow-up responses...

My Answer To Your Problem

posted by Jeffrey R Cohen:

To solve this problem you need to know that the length S of a side of a square is the square root of the area A of the square. Putting this into mathematical form we get,
S = sqrt(A) = sqrt(20000) = 141.4 feet.

[Note: "the square root of X" is denoted here as sqrt(X) because the normal square root symbol is not available in this screen]

Suppose you didn't know the formula for the length of a side of a square when only the area of the square is known. You could derive it as follows:
You know that the area A of a square is the length of any side S multiplied by itself. Expressed as a mathematical equation, this is
A = S*S
Now if we take the square root of both sides of the equation, we get
sqrt(A) = sqrt(S*S).
Now the definition of a square root is the number that is multiplied by itself is the square root of the product. So here the product is S*S, and the number that is multiplied by itself is S, so S is the square root of S*S. Now substituting S on the right side of the equation we get,
sqrt(A) = S.
Now just reverse the order of this equality and we get,
S = sqrt(A)
which is the formula we used.
Jeff Cohen

Square Footage

posted by carol:

room measures 12feet by 12feet and 7foot 6inches high, what is the square footage of this area