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If the altitude of a triangle increases by 6% and the base of the tria

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Bunuel
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If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   22 Jan 2020, 02:23
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If the altitude of a triangle increases by 6% and the base of the triangle increases by 8%, by what percent will the area of the triangle increase?

A. 6%
B. 8%
C. 7.24%
D. 14.48%
E. 48%
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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   22 Jan 2020, 03:15
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Original length - x
Original base - y

New length - 1.06x
New base - 1.08y

Percent change in area = ((1.06*1.08)xy - xy)/(xy)

= 14.48%

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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   22 Jan 2020, 23:50
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It's just like increasing the value of an investment by 6%, then by 8%. Since there's compounding, the answer will be slightly greater than 14%, so only D makes sense.
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MartinM94
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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   30 Jan 2020, 07:22
Can anyone explain how come when 10 cm is used for both the base and the altitude, the answer is different?
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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   30 Jan 2020, 07:32
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MartinM94 wrote:
Can anyone explain how come when 10 cm is used for both the base and the altitude, the answer is different?


The numbers you use won't matter here, so if you're not getting the correct answer for a certain set of numbers, there's a mistake in the calculation you're doing.
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If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   30 Jan 2020, 07:43
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Area = 1/2 * Base * Height

Since the base and height are multiplied,vwr can use the successive percent change formula:

If \(A = B * C\)
and say, percent change of B is x% and C is y%, percent change of A is simply:

\((x + y + xy/100)\)%

In this question, height of the triangle increases by 6% and the base of the triangle increases by 8%

Thus: \(x = 6\) and \(y = 8\)

Thus, percent change in area

\(= 6 + 8 + 6*8/100\)

= 14.48%

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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink] New post   30 Sep 2022, 09:36
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Re: If the altitude of a triangle increases by 6% and the base of the tria [#permalink]
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