I’m putting together a list of dimensions to do a vendor comparison so I’m trying to standardize some data sets and I’d like to find a way to automate this calculation.
We’re assuming that the dimensions of each store are 2:1 and I have the square footage for each store. I can brute force approximations but there are 500 stores and there must be a way to do this mathematically. Help?
You’re trying to solve the equation (2x)(1x) = sqft, which is the same as 2x[sup]2[/sup] = sqft, which can be solved in the usual way for a quadratic equation.
For example, given 800 square feet, 2x[sup]2[/sup] = 800 gives the solutions 20 and -20. We can safely ignore -20 since I assume you don’t want to build any negative stores. So your dimensions would be 20x40, which is 800 square feet.
Call the width w.
Call the length 2w (that’s “2 times w”, since it’s 2:1)
area = 2w[sup]2[/sup]
So, w = sqrt(area/2) (that’s a square root)
So, a 4000 sq ft floor would have width equal to sqrt(4000 sq ft / 2) = 44.7 ft and a length twice that, or 89.4 ft.
Translating into English: Halve your area, take the positive square root - that’s the short side; the long side is twice the short side.
Excel has a SQRT( number ) function.
Spreadsheet is an easy way to automate this.
now THAT’S what every math class should be like…!!!
If teachers would explain things this way, millions of people wouldn’t despise and fear mathematics.
It’s an excellent description of what to do but it doesn’t teach you anything and is simply a recipe for this one specific problem. friedo’s explanation might be longer and includes equations but actually teaches you how to do it. (Equations to solve a math problem? I’m shocked! Shocked!) That explanation can actually lead you to figure out a more general solution to apply to any shape room.
How odd I was sure I posted a thanks on this last night but it’s gone.
Anyway, I had initially set up the formula to find the square root of the area first and then divide that into the length and width. That did not work but both Friedo’s and Malacandra’s explainations made creating the excel formula easy 
Thanks so much everyone!
So is your preferred method of teaching the general solution of quadratic equations might be something like, “the quotient of the additive inverse of the coefficient of the linear term, plus or minus the square root of the difference of the square of the coefficient of the linear term and four times the coefficient of the quadratic term times the constant term, divided by twice the coefficient of the quadratic term.”
That’s precisely how it was taught for a long time. Not surprisingly, mathematics did not progress very far in the thousand or more years since the general solution was known.
Writing things in English is fine, but there are many good reasons to use mathematical notation. The language that it gives us allows us to express ideas in a vastly more efficient way. A student with a good command of algebra can not only memorize the quadratic formula easily, he can understand its derivation - where it comes from - after a five-minute demonstration. Writing the same derivation in English would take a book.
So I disagree that giving specific recipes in English is what every math class should be like. There are times for recipes and there are times to learn underlying concepts which can be applied later. As CookingWithGas points out, Malacandra’s method works fine in this case, but doesn’t teach anyone how to solve the problem again with different parameters. What if you want a 3:1 room or 5:4? What if you want to calculate volumes instead of areas? The answer I gave shows how you can derive solutions for those cases.