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April 2nd, 2007, 08:09 AM   #1
atw
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Calculating Width & Height of a rectange...?

Hi,

This is my first post so please be gentle and please move this post if I have posted it in the wrong place

I work for a real estate company and we were recently supplied with a diagram of an apartment and its total area (sq ft). From the diagram we figured out that the room was at a ratio of 1:3 (in the diagram the room was 1cm by 3cm). Eventually, I figured out the formula to work out the width and height from the ratio / area:
Code:
((AREA / 3) √ =WIDTH) * 3 = HEIGHT
This formula works fine as long as the room is of a nice ration like 1:3 or 1:2 or 1:4 etc because I can divide it up into squares.

Sorry for the long preamble. My question is, how would I calculate the width & height for a room / apartment with a less friendly ratio (one which wouldn't allow me to chop it into squares)?

Thanks in advance


PS. I am horrendously poor at Maths
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April 2nd, 2007, 12:47 PM   #2
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height/width = ratio

real height = measured height * x
real width = measured wdith * x

area = (measured height * conversion factor x) * (measured width * conversion factor x)

So, if you know that the ratio of the height to the width of the room is, say, 113/745, and you are told that the area of the room is 34 square feet, then how high and wide is the room?

area = (measured height * conversion factor x) * (measured width * conversion factor x)

34 = (113x)*(745x)

34 = (84,185)x²

√(34/84,185) = x

x = 0.0200965774

So, each side must be multiplied by x, and then the final units will be in square feet, and everything will work out.

real width = 745 * 0.0200965774 = 14.972 ft

real height = 113 * 0.0200965774 = 2.271 ft

We can backcheck and see if these values work:

area = 34 ft²

14.972 ft * 2.271 ft = 34 ft² CHECK


height/width = 113/745 = 0.15168

2.271 ft / 14.972 ft = 0.15168 CHECK

Note that it doesn't matter which side of the room you pick as the height or the width, as long as the sides you choose are at right angles to each other.

Quote:
PS. I am horrendously poor at Maths
That, my friend, can always be remedied. You can always further your mathematics education on your own. Mathematics is so much fun!
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April 2nd, 2007, 12:57 PM   #3
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Let's call the area of a room A, the length l, the width w, and the ratio of length to width (l/w) R. Since we know A and R, we want to find length and width in terms of these numbers. First, we want to get the length in terms of the width. By the way R was defined above, l=wR. The area of a rectangle is length times width, which is lw, or w²R. Now, since we know A and R, we want to solve for w.

A=lw
A=Rw²
w²=A/R
w=√(A/R)

Now we have a formula to find the width in terms of the area and ratio (make sure that the ratio is of length/width form, not the other way around!), we can simply find the length by multiplying the width by this ratio. In fact, we can even write the length in terms of A and R!

l=wR
l=R√(A/R)
l=√(AR²/R)
l=√(AR)

We now have two equations that can be used to find the length and width of a rectangular room given the area of the room and the ratio of length to width.

EDIT: Infinity seems to have snuck in a post while I was typing. One of the nice things about mathematics is that there are often several equally valid ways to solve a problem (and they yield the same answer!).
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April 2nd, 2007, 02:23 PM   #4
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Quote:
EDIT: Infinity seems to have snuck in a post while I was typing. One of the nice things about mathematics is that there are often several equally valid ways to solve a problem (and they yield the same answer!).
You just used a couple general equations to get the solution, while I used smaller sub equations. Either way works.
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May 17th, 2007, 01:21 PM   #5
atw
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OMG, I thought I had replied to this. Sorry.

Thank you very, very, very much for the help.

Again, sorry for not responding...
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May 18th, 2007, 03:23 AM   #6
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Do all real estate companies refer to a room's length as its height?
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May 18th, 2007, 06:20 AM   #7
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Quote:
Thank you very, very, very much for the help.
I always enjoy getting cubic appreciation.
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