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If the altitude of a triangle increases by 6%

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HKD1710
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If the altitude of a triangle increases by 6% [#permalink] New post   10 Mar 2017, 23:07
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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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D
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   10 Mar 2017, 23:15
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HKD1710 wrote:
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%


b --- base
h----- height
original area =bh/2

altitude of a triangle increases by 6% and the base of the triangle increases by 8%
b1 ---- new base
h1 ---- new height

new area = (b1*h1)/2 = (b*1.08*h*1.06)/2 = (bh/2)*(1.06*1.08) = original area * 1.1448

therefore the area of the triangle increases by 14.48 %

Hence option D is correct
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   06 May 2017, 18:03
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HKD1710 wrote:
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%


We can let the original base = b and the original altitude = a, and thus the original area is ab/2.

The new altitude is 1.06a and the new base is 1.08b, so the new area is 1.1448ab/2. The new area is 1.1448, or equivalently, 114.48% times the old area. Therefore, the area increased 114.48 - 100 = 14.48%.

Answer: D
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   11 Mar 2017, 01:16
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HKD1710 wrote:
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%


Percentage increase in the area of the triangle will be -

= \(6 + 8 + \frac{(6*8)}{100}\)

= \(14 + 0.48\)

= \(14.48\)

Thus, answer must be (D) 14.48 %
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   10 Mar 2017, 23:20
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HKD1710 wrote:
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%


Let's assume base 100 and height 100
So, area will be 0.5 * 100 * 100 ---(1)

Now with 6% increase in height and 8 % in base
New area 0.5* (100+6)*(100+8)=(100*100+100*8+100*6+6*8) ---(2)

percentage increase = (2)-(1)/(1) *100 = (100*8+100*6+6*8) *100 /(100*100) =14.48%

In general if the is x% increase in a and y % increase in b then overall % increase in ab will be (x+y+(xy)/100)

Kudos please if you find useful :-)
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   04 May 2017, 02:18
Abhishek009 wrote:
HKD1710 wrote:
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%


Percentage increase in the area of the triangle will be -

= \(6 + 8 + \frac{(6*8)}{100}\)

= \(14 + 0.48\)

= \(14.48\)

Thus, answer must be (D) 14.48 %


Can you explain how do we arrive at 6+8+fraction.. ..the concept
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If the altitude of a triangle increases by 6% [#permalink] New post   04 May 2017, 13:11
HKD1710 wrote:
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%


base triangle area=.5*1*1=.5
enlarged triangle area=.5*1.06*1.08=.5724
.5724/.5=1.1448=14.48% increase
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Re: If the altitude of a triangle increases by 6% [#permalink] New post   20 Aug 2022, 21:09
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Re: If the altitude of a triangle increases by 6% [#permalink]
20 Aug 2022, 21:09
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