January 2nd, 2014, 08:05 AM  #1 
Newbie Joined: Dec 2013 Posts: 18 Thanks: 0  Geometry percent change
If the length of the base of a triangle is increased by 10 percent and the height is decreased by 20 percent, what is the percent decrease in the area of the triangle? (A) 6% (B) 8% (C) 10% (D) 12% 
January 2nd, 2014, 10:18 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,378 Thanks: 730  Re: Geometry percent change
WHAT have you tried? Do you know that trying to get your homework done is CHEATING? Is your teacher aware you're doing this? 
January 2nd, 2014, 10:25 AM  #3  
Member Joined: Dec 2013 Posts: 82 Thanks: 0  Re: Geometry percent change Quote:
where h = height and b = base. Let's say for a start that This could be a triangle with a height of 2 and base of 2. If we increase the length of the base by 10% the area will now be? And if we then decrease the height by 20% then area will now be? So what percentage has it decreased by?  
January 2nd, 2014, 12:03 PM  #4  
Newbie Joined: Dec 2013 Posts: 18 Thanks: 0  Re: Geometry percent change Quote:
provide succinct explanations for vast majority of problems. It is also to my surprise how one could POSSIBLY come to a conclusion in a matter of seconds.You may be excused.  
January 2nd, 2014, 01:57 PM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,378 Thanks: 730  Re: Geometry percent change Quote:
2: too bad you didn't advise of your situation right off the start...or did you and I missed it? Happy new year.  
January 2nd, 2014, 02:19 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,433 Thanks: 1462 
Even if it were homework, [color=#00AA00]Denis[/color], it's not necessarily cheating, because (a) the correct answer was not demanded in the post, (b) finding the answer by any means may have been permitted, or (c) the answer could be submitted together with a note about how it was obtained. In response to such a question, it's reasonable, and probably more helpful, to explain how percentages are calculated and used for questions of this type. Alternatively, you could just ask about what has been attempted, where difficulty was encountered, etc. The problem is equivalent to asking for the overall change when some nonzero value is changed first by a, then by b, where a and b are expressed as percentages  specifically (for this particular problem), a = 10% = 0.1 and b = 20% = 0.2. Using the above approach, we need to (1) justify the equivalence, and (2) apply a "formula" (or method) for combining a and b. I'm not sure whether any textbooks give the relevant formula, but it is a + b + ab. 
January 2nd, 2014, 04:47 PM  #7  
Banned Camp Joined: Dec 2013 Posts: 34 Thanks: 1  Re: Geometry percent change Quote:
 
January 2nd, 2014, 05:18 PM  #8  
Banned Camp Joined: Dec 2013 Posts: 34 Thanks: 1  Re: Geometry percent change Quote:
We are told our dimensions have been scaled. Recall that "percent" means "perhundred". That means 10% = 10/100 = 0.10 and 80% = 80/100 = 0.80 (100%20% = 80%) (alternatively you can move the decimal point of any percent you are given to the left TWICE and omit the "%" symbol) Now we can rewrite our formula for Area. I will reduce both fractions: Area = ½(Base)(Height) do NOT combine fractions with the ½; that needs to stay there to represent A in its original form. Putting our scaling factor in front, it is easy to see that our new Area is the original Area times the product of both scaling factors:  
January 2nd, 2014, 05:29 PM  #9  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,378 Thanks: 730  Re: Quote:
But we can see at this site very different ways: some provide the full answer right off the bat others do NOT, and insist on the OP showing work Anyhow, my intent is not to rock the boat. Most other similar sites have a "Read before posting" section, where it is indicated that no help will be given unless some work is shown...  
January 2nd, 2014, 05:37 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,433 Thanks: 1462 
Unfortunately, chameleojack, your assumptions are incorrect, and so your answer is also incorrect. On this site, by the way, omitting a specific request as to what help you want does not imply that "just the answer" is wanted. Sometimes, "just the answer" is posted in reply, but that is usually intended to encourage further work by the original poster, as problems tend to seem more worthwhile if the correct final result is known in advance. Sometimes, just the answer is given because finding that answer from scratch is rather tedious or difficult, but verifying that it's correct is relatively easy. 

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