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 Post subject: GRE Geometry (Numerical Entry)
PostPosted: Fri Sep 23, 2011 11:51 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
A scale drawing of a rectangular garden plot measures 5 inches by 7 inches. If the longer side of the garden plot is 21 feet, what is the area, in square feet, of the actual garden plot?

The correct answer is 315.

You can solve this quickly by setting up a ratio: 5/7 = x/21. Cross multiplying yields 105 = 7x, so x = 15, which is the width. Now find the area = length × width, and you get area = (21)(15) = 315 square feet.
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The length of the garden is expressed in feet. Thus the lenght of the area in inches is 21 × 12 = 252. The proportion becomes: 5/7 = x/252, and the value of x so found is 180. The area of the actual garden plot is:
180 × 252 = 45360 squared inches which in feet is 3780.


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 Post subject: Re: t.4 s.4 qt.13: geometry, proportions
PostPosted: Fri Sep 23, 2011 12:04 pm 
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Quote:
180 × 252 = 45360 squared inches which in feet is 3780
It is perfectly okay to do what you did, to convert the 21 feet into 252 inches. And your area of 45,360 square inches is also correct for the area of the garden plot, in square inches. But, in order to convert back to square feet, you must divide, NOT by 12, but by 144. There are 144 square inches in one square foot, and thus the math becomes 45,360/144, which still yields 315 square feet.


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 Post subject: Re: t.4 s.4 qt.13: geometry, proportions
PostPosted: Wed May 02, 2012 4:15 am 
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Don't you need to convert inches to feet before creating the proportions? I converted 5 in. to .41 ft, 7 in. to .58 ft, then created the proportion to cross multiply and solve for x, which came to 14.8 – my area was 311.7 and wrong. Why so? Isn't mine more accurate?


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 Post subject: Re: t.4 s.4 qt.13: geometry, proportions
PostPosted: Wed May 02, 2012 4:16 am 
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Isn't mine more accurate?

You make approximations along the way, while the explanation deals with exact numbers. Thus the correct answer is the exact value, while yours is an approximation. You may try to convert feet in the right side into inches instead of converting inches in the left side into feet.

Quote:
Don't you need to convert inches to feet before creating the proportions?

That is a good question indeed. If the units relate with some fixed coefficient, e.g. 1 foot = 12 × 1 inch, 1 meter = 100 × 1 cm, then that coefficient will be simplified in the fraction when we convert.

5 inch /7 inch = (x × 12) inch / (21 × 12) inch

Common length units relate in such manner. However, if we had a proportion defined for Celsius degrees, while a value given in Fahrenheit degrees, then we would have to convert the value into Celsius degrees before plugging it in. (C = (F – 32) × 5/9)


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