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Friday, July 16, 2010

Drawing to Scale, Part 2

This blog is all about using elementary math in our grown-up lives. Yesterday I left you hanging with a question:

Q1. If on a scale drawing 1 inch equals 32 inches, what scale distance equals 12 inches (1 foot)?

A1. Here's how we find the answer:

1.5 inches on the paper equals 48 inches in real life, so 1.0 inches equals 32 inches (48 ÷ 1.5 = 32)

We want to know what fraction of 1 inch equals 12 inches in real life. 
That is an unknown value which I will call X.

X is to 1 what 12 is to 32, or to say it another way, X÷1 = 12÷32

First we simplify the right side - the largest common denominator of 12 and 32 is 4. 
We find 4 goes into 12 three times and 4 goes into 32 eight times.


To simplify the left side we just throw away the 1, because X÷1 = X 

Now we have X = 3/8

The answer is 3/8" on paper is equal to 12" in real life

To check our answer we could ask how many of those 3/8s are there in 12 inches?
One way to do this is to convert 3/8 to a decimal number.
Divide 8 into 1.00 and you get .125 then multiply by 3 and you have .375
Now we do the division 12 ÷ .375 = 32 which is where we started (1 inch equals 32 inches)

Whew! Why go through such complications? Why not scale 1:10 or something simple? Well, we use this scale because you can show a typical room or two of a house on one piece of paper.

Q2. Assume an inch of margin on all sides of a sheet of 8 1/2" x 11" paper. What is the largest room that can be drawn on this paper at 1:32 scale? Round the answer to the nearest foot.

A2. Subtract the margins to find remaining space, and calculate the largest scaled room that will fit.

(8.5 - 2 = 6.5) and (11-2 = 9) so 6.5 inches x 9 inches is the free space for drawing a room.

6.5 x 32 (our scale) = 208 inches       Divide 208 ÷ 12 = 17 feet 4 inches which we round to 17

9 x 32 = 288 inches     Divide 288 ÷ 12 = 24 feet 0 inches

The largest room that will fit on this paper is 17 x 24 feet.