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# A parallelogram has perimeter 16 and base of length 5. Which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 60584
A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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22 Sep 2017, 00:41
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A parallelogram has perimeter 16 and base of length 5. Which of the following could NOT be the area of the parallelogram?

(A) 20
(B) 15
(C) 10
(D) 4
(E) 1

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Re: A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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20 Jun 2018, 17:07
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Bunuel wrote:
A parallelogram has perimeter 16 and base of length 5. Which of the following could NOT be the area of the parallelogram?

(A) 20
(B) 15
(C) 10
(D) 4
(E) 1

Since a parallelogram has two sets of equal-length opposite sides, we have:

2a + 2b = perimeter

2a + 2(5) = 16

2a = 6

a = 3

The two adjacent sides, i.e., the two sides that have different lengths, are 5 and 3. Even if these two sides are perpendicular, i.e., the parallelogram is a rectangle, the area is at most 5 x 3 = 15. If they are not perpendicular, the area would be less than 15. Therefore, the area of the parallelogram can’t be 20 since the area can’t be more than 15.

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Re: A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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22 Sep 2017, 01:42
A parallelogram has perimeter 16 and base of length 5. Which of the following could NOT be the area of the parallelogram?

Perimeter = 16 and base =5
=> 2nd side =x => 2(5+x)=16 => x= 3
So parallelogram sides = 5 and 3

The area of parallelogram is maximized if its a rectangle => maximum area = 5*3 =15

Answer: A <=value is greater than maximum possible area
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Re: A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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21 Nov 2019, 23:03
If the base is 5, then the perimeter is given as 2 (B+L) = 2(5+L) = 16

=> L= 3. In this case, the area will be maximum as a rectangle.

=> the area cannot exceed l*b = 15. => 20 is not possible.

Ans A
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Re: A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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22 Nov 2019, 23:43
I understand how 20 is not possible. How is 1 possible ?
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Re: A parallelogram has perimeter 16 and base of length 5. Which of the  [#permalink]

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24 Nov 2019, 00:32
Amlu95 wrote:
I understand how 20 is not possible. How is 1 possible ?

Area is base x height, height can be minimised to achieve 1.

I think you are assuming area as base x length.

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Re: A parallelogram has perimeter 16 and base of length 5. Which of the   [#permalink] 24 Nov 2019, 00:32
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