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# If the perimeter of a rectangular garden plot is 38 feet and its area

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Math Expert
Joined: 02 Sep 2009
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If the perimeter of a rectangular garden plot is 38 feet and its area  [#permalink]

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23 Aug 2018, 04:01
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15% (low)

Question Stats:

88% (01:33) correct 12% (02:06) wrong based on 42 sessions

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If the perimeter of a rectangular garden plot is 38 feet and its area is 84 square feet, what is the length of the shorter sides?

A. 4
B. 7
C. 12
D. 14
E. 24

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Re: If the perimeter of a rectangular garden plot is 38 feet and its area  [#permalink]

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23 Aug 2018, 04:16
Bunuel wrote:
If the perimeter of a rectangular garden plot is 38 feet and its area is 84 square feet, what is the length of the shorter sides?

A. 4
B. 7
C. 12
D. 14
E. 24

Given, perimeter=38
Or, 2(l+w)=38----(1)

Given, area=84
Or, l*w=84=12*7
Or, l=12, w=7
This also satisfies eq(1).

So, length of shorter side is 7 unit.

Ans. (B)
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Re: If the perimeter of a rectangular garden plot is 38 feet and its area  [#permalink]

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25 Feb 2019, 06:44
1
We have 2 equations:
2(l+w) = 38 --> l+w = 19
l*w = 84

Faster way: prime factoring 84 and picking answer that equals 19
84 --> 42*2 --> 21*2^2 --> 3*7*2²

A) short side = 4, long side = 21 (from remaining factors 3*7), 4+21 ≠ 19
B) short = 7, long = 12 (from remaining 3*2²), 7+12 = 19

from l*w=84 --> l = 84/w
from l+w = 19 --> 84/w + w = 19
84 + w² = 19w
w² - 19w + 84 = 0
(w - 7)(w - 12) = 0
w = 7, 12
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Re: If the perimeter of a rectangular garden plot is 38 feet and its area  [#permalink]

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25 Feb 2019, 07:58
Bunuel wrote:
If the perimeter of a rectangular garden plot is 38 feet and its area is 84 square feet, what is the length of the shorter sides?

A. 4
B. 7
C. 12
D. 14
E. 24

$$2(L + B) = 38$$

So, $$L + B = 19---------------(I)$$

$$L*B = 84----------------(II)$$

Now, L can be 12 and B can be 7 to satisfy both (I) & (II)

Thus, Answer must be (B) 7
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Re: If the perimeter of a rectangular garden plot is 38 feet and its area  [#permalink]

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27 Feb 2019, 10:26
Bunuel wrote:
If the perimeter of a rectangular garden plot is 38 feet and its area is 84 square feet, what is the length of the shorter sides?

A. 4
B. 7
C. 12
D. 14
E. 24

We can create the equations:

2L + 2W = 38

L + W = 19

L = 19 - W

and

LW = 84

Substituting, we have:

(19 - W)W = 84

19W - W^2 = 84

W^2 - 19W + 84 = 0

(W - 7)(W - 12) = 0

W = 7, so L = 12

or

W = 12, so L = 7

In either case, the shorter side is 7.

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Re: If the perimeter of a rectangular garden plot is 38 feet and its area   [#permalink] 27 Feb 2019, 10:26
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