If the length of each side of an equilateral triangle were increased : Problem Solving (PS)

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If the length of each side of an equilateral triangle were increased

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If the length of each side of an equilateral triangle were increased [#permalink]

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23 Oct 2018, 20:05

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55% (hard)

Question Stats:

52% (01:03) correct

48% (01:25) wrong

based on 47 sessions

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If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?

A. 75%
B. 100%
C. 125%
D. 150%
E. 225%

Spoiler: OA

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If the length of each side of an equilateral triangle were increased [#permalink]

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23 Oct 2018, 20:20

Bunuel wrote:

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?

A. 75%
B. 100%
C. 125%
D. 150%
E. 225%

Area of Equilateral Triangle \(= (\frac{√3}{4})*Side^2\)

Let, Side = 4

Earlier Area of Equilateral Triangle \(= (\frac{√3}{4})*4^2 = 4√3\)

After 50% increase in side Area of Equilateral Triangle \(= (\frac{√3}{4})*6^2 = 9√3\)

Percentage Increase = (Final Value - Initial Value)*100 / Initial Value \(= (9√3 - 4√3)*100/(4√3) = 125\)

Answer: Option C
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Re: If the length of each side of an equilateral triangle were increased [#permalink]

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23 Oct 2018, 21:07

Let the length of each side be 'a'

So the area of the triangle is A = \(\sqrt{3}\)/4 \(a^2\)

Now the side is increased by 50% i.e, \(a\) becomes \(1.5a\)

So the area becomes \(\sqrt{3}\)/4 \((1.5a)^2\)

= \(\sqrt{3}\)/4 * \(2.25a^2\)

= 2.25 * \(\sqrt{3}\)/4 \(a^2\)

= 2.25 * A

The area became 2.25 times the initial area, in turn, 125% more than the original area.

OPTION: C
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Re: If the length of each side of an equilateral triangle were increased [#permalink]

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23 Oct 2018, 22:52

Bunuel wrote:

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the area?

A. 75%
B. 100%
C. 125%
D. 150%
E. 225%

\(50 + 50 + \frac{50*50}{100}\)

= \(125\); Answer must be (C)
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