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# If the length and width of a rectangular garden plot were each increas

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Math Expert
Joined: 02 Sep 2009
Posts: 51188
If the length and width of a rectangular garden plot were each increas  [#permalink]

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09 Nov 2017, 22:25
00:00

Difficulty:

15% (low)

Question Stats:

87% (00:48) correct 13% (00:57) wrong based on 71 sessions

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If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

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Posts: 3325
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Re: If the length and width of a rectangular garden plot were each increas  [#permalink]

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10 Nov 2017, 00:05
Bunuel wrote:
If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Let the length of the rectangular plot be x and the width be y.
The area of this plot is xy.

If the length and breadth of the rectangular plot were to increase by 20% each,
the length and width will be 1.2x and 1.2y. Therefore, the area will be 1.44xy

Hence, the area increase by 44%(Option E)
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Re: If the length and width of a rectangular garden plot were each increas  [#permalink]

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11 Nov 2017, 05:08
2
pushpitkc wrote:
Bunuel wrote:
If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Let the length of the rectangular plot be x and the width be y.
The area of this plot is xy.

If the length and breadth of the rectangular plot were to increase by 20% each,
the length and width will be 1.2x and 1.2y. Therefore, the area will be 1.44xy

Hence, the area increase by 44%(Option E)

easy way to solve above is to consider length equals 100, Breadth equals 100.
Increased by 20%.. length equals 120 breadth equals 120
Area difference = 4400
percentage is 44
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Re: If the length and width of a rectangular garden plot were each increas  [#permalink]

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11 Nov 2017, 07:45
1
Bunuel wrote:
If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%
0
$$20+20+\frac{20*20}{100}$$

= $$44$$%

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If the length and width of a rectangular garden plot were each increas  [#permalink]

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11 Nov 2017, 16:03
Bunuel wrote:
If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

A square is a rectangle.
W = 10
L = 10
Original area: (L*W) = (10 * 10) = 100

Length and width are both increased 20 percent:

W = (10 * 1.2) = 12
L = (10 * 1.2) = 12
New area: (L*W) = (12 * 12) = 144

Percent increase in the area:

$$\frac{New-Old}{Old} * 100$$

$$\frac{144- 100}{100}=\frac{44}{100}= (.44 * 100)$$ = 44 percent

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Re: If the length and width of a rectangular garden plot were each increas  [#permalink]

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14 Nov 2017, 06:13
Bunuel wrote:
If the length and width of a rectangular garden plot were each increased by 20 percent, what would the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

If we let L = the original length and W = the original width, then the original area of the rectangle is LW.

The new area is 1.2L x 1.2W = 1.44LW.

Thus, we see that there is a 44% increase in the area.

Alternate Solution:

We can let the original length = 10 and the original width = 10. We see that the increased length will be 12 and the increased width will be 12.

The original area is length x width = 10 x 10 = 100. The new area is 12 x 12 = 144.

We find the percentage increase in the area by using the formula (new – old)/old x 100, and we obtain:
(144 – 100)/100 x 100 = 44/100 x 100 = 44%.

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Re: If the length and width of a rectangular garden plot were each increas &nbs [#permalink] 14 Nov 2017, 06:13
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