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A triangle has a base length of 14 cm and a height of 10 cm. The base

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MathRevolution
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A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink] New post   01 Jul 2020, 01:33
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[GMAT math practice question]

A triangle has a base length of \(14 cm\) and a height of \(10 cm.\) The base length increases by \(10\%\), and the height decreases by \(10\%. \) What will the area of the triangle be?

A. Increases by \(0.5 cm^2\)

B. Decreases by \(0.7 cm^2 \)

C. Increases by \(0.9 cm^2\)

D. Decreases by \(0.3 cm^2\)

E. Decreases by \(0.5 cm^2\)
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B
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Re: A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink] New post   01 Jul 2020, 01:49
Area of original triangle = 1/2*base*height
=> 1/2*14*10
=> 70

Now, the base length increases by 10% and height decreases by 10%
New height = 10*90/100 = 9
and base = 14*110/100 = 15.4

Area of new triangle= 1/2*15.4*9 = 69.3

The new triangle length is decreasing by 0.7 points.

MathRevolution I think B option has Decreasing by 0.7 instead of increasing. Kindly check.

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Re: A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink] New post   01 Jul 2020, 02:00
given : base of triangle 14 cm and height of triangle 10 cm
thus area = 1/2*14*10=70 cm^2
now base increase by 10% which is 15.4 cm and height decrease by 10% which is 9 cm
so new area will be 1/2* 15.4*9 = 69.30c m^2
70-69.30=0.70 cm^2

don't care about increase decrease because only one option has 0.07 in it
ANS:B
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Re: A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink] New post   01 Jul 2020, 11:47
Original area = 0.5*14*10 = 70
New area = 0.5*15.4*9 = 69.3
Difference = 70-69.3 = 0.7

Answer is B (although it is a decrease, so the given answer is wrong)
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Re: A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink] New post   03 Jul 2020, 02:51
Expert Reply
=>

The area of the original triangle is \((\frac{1}{2})·14·10 = 70.\)

The area of the modified triangle is \((\frac{1}{2})·(14·(1 + 0.1))·(10·(1 - 0.1)) = (\frac{1}{2})·14·10·(1 + 0.1)·(1 - 0.1) = 70·(1 - 0.01) = 70 – 0.7.\)

Thus, the area decreases by \(0.7.\)

Therefore, B is the correct answer.
Answer: B
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gmatclubot
Re: A triangle has a base length of 14 cm and a height of 10 cm. The base [#permalink]
03 Jul 2020, 02:51
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