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

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Math Expert
Joined: 02 Sep 2009
Posts: 44282
If the area of a square increases by 69 percent, then the side of the [#permalink]

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02 Nov 2017, 02:54
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35% (medium)

Question Stats:

64% (00:44) correct 36% (00:33) wrong based on 45 sessions

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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%
[Reveal] Spoiler: OA

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

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02 Nov 2017, 03:36
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%

Formula used: Area of square = $$(Side)^2$$
If the area of the square increases by 69%, the side will increase by 30%

Lets assume the side of the square to be 10 units, making area 100 units!
The area increase by 69%, the new area will be 169 units.

Hence, the area will be $$\sqrt{169}$$ or 13 units.
This is a thirty percent increase in the square's side(Option 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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02 Nov 2017, 04:08
pushpitkc wrote:
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%

Formula used: Area of square = $$(Side)^2$$
If the area of the square increases by 69%, the side will increase by 30%

Lets assume the side of the square to be 10 units, making area 100 units!
The area increase by 69%, the new area will be 169 units.

Hence, the area will be $$\sqrt{169}$$ or 13 units.
This is a thirty percent increase in the square's side(Option B)

Agree..alternatively

a + a + a^2/100 = 69%
2a + (a^2)/100 = 69%
hence a is 30
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Posts: 1416
If the area of a square increases by 69 percent, then the side of the [#permalink]

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02 Nov 2017, 16:20
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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

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

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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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05 Nov 2017, 08:23
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.

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Re: If the area of a square increases by 69 percent, then the side of the   [#permalink] 05 Nov 2017, 08:23
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