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 January 2nd, 2014, 07:05 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, 09:18 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,126 Thanks: 800 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, 09:25 AM   #3
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Re: Geometry percent change

Quote:
 Originally Posted by Rfeynman16 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%
Well the formula for the area of a triangle is

$A=0.5hb$

where h = height and b = base. Let's say for a start that

$0.5hb=2$

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, 11:03 AM   #4
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Re: Geometry percent change

Quote:
 Originally Posted by Denis WHAT have you tried? Do you know that trying to get your homework done is CHEATING? Is your teacher aware you're doing this?
For your information Denis, I am studying for an ISEE entrance exam from a textbook that does not
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, 12:57 PM   #5
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Re: Geometry percent change

Quote:
 Originally Posted by Rfeynman16 For your information Denis, I am studying for an ISEE entrance exam from a textbook that does not 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.
1: concluded the way I did because it happens "most of the time"...
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, 01:19 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,845 Thanks: 1567 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 non-zero 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, 03:47 PM   #7
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Re: Geometry percent change

Quote:
 Originally Posted by Rfeynman16 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%
The reason people assume you are "cheating" is that you have 4 answers in front of you by nature of the question and only a lazy, LAZY person would state the question *ONLY* and not specify they wanted to learn something. Your silence implies you want "just the answer", just as your first post has "just the question".

January 2nd, 2014, 04:18 PM   #8
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Re: Geometry percent change

Quote:
 Originally Posted by Rfeynman16 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%
Area = ½(Base)(Height)

We are told our dimensions have been scaled. Recall that "percent" means "per-hundred". 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)

$A=\frac{1}{2}(\frac{10}{100}l)(\frac{80}{100}h)$
$A=\frac{1}{2}(\frac{1}{10}l)(\frac{4}{5}h)$
$A=\frac{1}{2}\cdot\frac{2}{25}(l)(h)$
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:
$A=\frac{2}{25}\cdot\frac{1}{2}(l)(h)$
$A_n_e_w=\frac{2}{25}A_0$

January 2nd, 2014, 04:29 PM   #9
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Re:

Quote:
 Originally Posted by skipjack 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........
I hear you Skip; nice in theory...
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...

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# The height of a triangle increased by 20% how much does the height need to decrease so the area will stay the same

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