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If the area of a square increases by 69 percent, then the side of the [#permalink]
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Bunuel wrote:
If the area of a square increases by 69 percent, then the side of the square increases by

(A) 13%
(B) 30%
(C) 39%
(D) 69%
(E) 130%

Choose numbers
Original square, A, area = 100
New big square, B, area = 169

Area = s\(^2\). Area of A = 100. Area of B = 169
Side A = \(\sqrt{100} = 10\)
Side B = \(\sqrt{169} = 13\)

Percent increase in side length:
\(\frac{New-Old}{Old}*100\)

\(\frac{(13-10)}{10}=\frac{3}{10}=.3 * 100 =\) 30 percent

Answer B

Scale factor

The area of a square increases 69 percent = 1.69

Area = length * length
Both lengths increase by a scale factor, \(k\)
So new area equals (old area * \(k^2\))

\(k^2 = 1.69\)

\(k = \sqrt{1.69}\)

\(k = 1.3 =\) scale factor
Both sides of A were increased by the scale factor.

Percent increase in side length:
\(\frac{(New-Old)}{Old}*100\)

\(\frac{1.3-1}{1}=.3 * 100 =\) 30 percent

Answer B
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Re: If the area of a square increases by 69 percent, then the side of the [#permalink]
Expert Reply
Bunuel wrote:
If the area of a square increases by 69 percent, then the side of the square increases by

(A) 13%
(B) 30%
(C) 39%
(D) 69%
(E) 130%


Let’s let the side length of the original square = 10. Thus, the area of the original square = 100. Since the area of the square increases by 69 percent, the area of the new square = 169. Thus, the side length of the new square = √169 = 13, which is a 30% increase in the side length of the original square.

Answer: B
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Re: If the area of a square increases by 69 percent, then the side of the [#permalink]
Bunuel wrote:
If the area of a square increases by 69 percent, then the side of the square increases by

(A) 13%
(B) 30%
(C) 39%
(D) 69%
(E) 130%


Asked: If the area of a square increases by 69 percent, then the side of the square increases by

Area of a square = a^2 ; where a is side of the square

New area = \(1.69a^2 = (1.3a)^2 = (1 + .3)a^2\)

IMO B
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Re: If the area of a square increases by 69 percent, then the side of the [#permalink]
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Re: If the area of a square increases by 69 percent, then the side of the [#permalink]
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