# 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:*

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:*