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

Question

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

niks18 · Answer

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

Luckisnoexcuse · Answer

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)

niks18 · Answer

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?

Bunuel · Answer

No, the dimensions must be greater than 0.

niks18 · Answer

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

Bunuel · Answer

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

niks18 · Answer

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

JeffTargetTestPrep · Answer

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.

Answer: A

generis · Answer

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.

Answer (A)

JeffTargetTestPrep · Answer

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.

Answer: A

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards