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# If the perimeter of a rectangular garden plot is 80 meters, which of

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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26 Sep 2017, 23:25
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If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

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If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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Updated on: 27 Sep 2017, 05:50
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

$$2(l+b)=80 => l+b=40$$

Hence $$l=40-b$$, so length has to be less than $$40$$, because in GMAT side of a geometric figure is greater than 0

Option A

Originally posted by niks18 on 26 Sep 2017, 23:51.
Last edited by niks18 on 27 Sep 2017, 05:50, edited 1 time in total.
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Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 04:09
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Perimeter = 2L + 2B
If perimeter is 80 then 2L should be below 80
L should be below 40 (rectangle has L & B)

I only
A

Not D because if L is 40 then perimeter will be 80 + 2B in that case (breadth of rectangle will be 0)
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Luckisnoexcuse

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Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 04:21
Luckisnoexcuse wrote:
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Perimeter = 2L + 2B
If perimeter is 80 then 2L should be below 80
L should be below 40 (rectangle has L & B)

I only
A

Not D because if L is 40 then perimeter will be 80 + 2B in that case (breadth of rectangle will be 0)

Mathematically width/length of the rectangle can be negligible and hence can be 0. essentially it will be a straight line. I am not sure how GMAT geometry treats this.

Hi Bunuel

Can you give some insight as to whether breadth/length of a rectangle can be 0?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 04:33
niks18 wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Perimeter = 2L + 2B
If perimeter is 80 then 2L should be below 80
L should be below 40 (rectangle has L & B)

I only
A

Not D because if L is 40 then perimeter will be 80 + 2B in that case (breadth of rectangle will be 0)

Mathematically width/length of the rectangle can be negligible and hence can be 0. essentially it will be a straight line. I am not sure how GMAT geometry treats this.

Hi Bunuel

Can you give some insight as to whether breadth/length of a rectangle can be 0?

No, the dimensions must be greater than 0.
_________________
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Joined: 25 Feb 2013
Posts: 1182
Location: India
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Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 05:48
Quote:
Mathematically width/length of the rectangle can be negligible and hence can be 0. essentially it will be a straight line. I am not sure how GMAT geometry treats this.

Hi Bunuel

Can you give some insight as to whether breadth/length of a rectangle can be 0?

No, the dimensions must be greater than 0.

Hi Bunuel,

Thanks for clarifying and I agree that from GMAT stand point we can consider that a geometric figure must have dimensions because in GMAT concepts of calculus or complex numbers are not tested. Hence i will edit my solution accordingly.

But Mathematically there is a concept of Degeneracy Condition according to which a line segment is a degenerate condition of a rectangle as one of its side tends to 0

And in fact we have used this concept in GMAT Club forum -

https://gmatclub.com/forum/if-two-sides ... 41227.html
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 05:54
niks18 wrote:
Quote:
Mathematically width/length of the rectangle can be negligible and hence can be 0. essentially it will be a straight line. I am not sure how GMAT geometry treats this.

Hi Bunuel

Can you give some insight as to whether breadth/length of a rectangle can be 0?

No, the dimensions must be greater than 0.

Hi Bunuel,

Thanks for clarifying and I agree that from GMAT stand point we can consider that a geometric figure must have dimensions because in GMAT concepts of calculus or complex numbers are not tested. Hence i will edit my solution accordingly.

But Mathematically there is a concept of Degeneracy Condition according to which a line segment is a degenerate condition of a rectangle as one of its side tends to 0

And in fact we have used this concept in GMAT Club forum -

https://gmatclub.com/forum/if-two-sides ... 41227.html

You most definitely do not need consider degenerate polygons on the GMAT. The question you mention also does NOT consider degenerate triangles.
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Joined: 25 Feb 2013
Posts: 1182
Location: India
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Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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27 Sep 2017, 06:11
Bunuel wrote:
niks18 wrote:
Quote:
Mathematically width/length of the rectangle can be negligible and hence can be 0. essentially it will be a straight line. I am not sure how GMAT geometry treats this.

Hi Bunuel

Can you give some insight as to whether breadth/length of a rectangle can be 0?

No, the dimensions must be greater than 0.

Hi Bunuel,

Thanks for clarifying and I agree that from GMAT stand point we can consider that a geometric figure must have dimensions because in GMAT concepts of calculus or complex numbers are not tested. Hence i will edit my solution accordingly.

But Mathematically there is a concept of Degeneracy Condition according to which a line segment is a degenerate condition of a rectangle as one of its side tends to 0

And in fact we have used this concept in GMAT Club forum -

https://gmatclub.com/forum/if-two-sides ... 41227.html

You most definitely do not need consider degenerate polygons on the GMAT. The question you mention also does NOT consider degenerate triangles.

Yup got it . I mentioned this example because in this example as well as in similar examples some experts have assumed minimum area of triangle to be 0. so if that is possible then minimum area of rectangle can be 0 for this case.
But let's not harp on this further and its safe to assume that in GMAT area cannot be 0.
Thanks Bunuel for your great insights
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Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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29 Sep 2017, 11:20
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

We can create the following equation:

2W + 2L = 80

W + L = 40

L = 40 - W

Thus, we see that the length must be less than 40. The only answer choice that fits this criterion is Roman numeral I, 30 meters.

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If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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29 Sep 2017, 17:30
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

If 80 is the perimeter, to find the limits, assume length L is the long side of the rectangle.

2L < 80 meters (or there wouldn't be width)

L < 40 meters

Only Option I, 30 meters, works.

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Affiliations: Target Test Prep
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Posts: 2669
Re: If the perimeter of a rectangular garden plot is 80 meters, which of [#permalink]

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01 Oct 2017, 12:09
Bunuel wrote:
If the perimeter of a rectangular garden plot is 80 meters, which of the following could be the length of one of its sides?

I. 30 meters
II. 40 meters
III. 50 meters

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

We can create the following equation:

2W + 2L = 80

W + L = 40

L = 40 - W

Thus, we see that the length must be less than 40. The only answer choice that fits this criterion is Roman numeral I, 30 meters.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If the perimeter of a rectangular garden plot is 80 meters, which of   [#permalink] 01 Oct 2017, 12:09
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