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

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

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New post 22 Sep 2017, 00:41
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A
B
C
D
E

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  55% (hard)

Question Stats:

59% (01:33) correct 41% (01:30) wrong based on 63 sessions

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

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New post 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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New post 20 Jun 2018, 17:07
1
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.

Answer: A
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Re: A parallelogram has perimeter 16 and base of length 5. Which of the &nbs [#permalink] 20 Jun 2018, 17:07
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