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April 2nd, 2007, 08:09 AM  #1 
Newbie Joined: Apr 2007 Posts: 2 Thanks: 0  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 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 
April 2nd, 2007, 12:47 PM  #2  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
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:
 
April 2nd, 2007, 12:57 PM  #3 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
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!). 
April 2nd, 2007, 02:23 PM  #4  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
 
May 17th, 2007, 01:21 PM  #5 
Newbie Joined: Apr 2007 Posts: 2 Thanks: 0  OMG, I thought I had replied to this. Sorry. Thank you very, very, very much for the help. Again, sorry for not responding... 
May 18th, 2007, 03:23 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
Do all real estate companies refer to a room's length as its height?

May 18th, 2007, 06:20 AM  #7  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
 

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