A parallelogram has perimeter 16 and base of length 5.

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Mon Jun 18, 2018 2:16 am

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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

[spoiler]OA=A[/spoiler]

I don't know how to solve this PS question. <i class="em em-confused"></i>

Why is A? I don't understand. Please, help me.

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Source: Beat The GMAT — Problem Solving | Mon Jun 18, 2018 2:16 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon Jun 18, 2018 3:19 am

Hello Gmat_mission.

Let's see your question.

We know the following:
- The parallelogram has perimeter 16.
- The length of the base is 5.

Let "s" be the length of the other side of the parallelogram, hence we have that $$Perimeter=2base+2s\ \ \Rightarrow\ 16=2\left(5\right)+2s\ \Rightarrow\ s=3.$$ Now, the parallelogram with the largest area is the rectangle.

If we assume that the given parallelogram is a rectangle, then its area is equal to $$Area=5\cdot3=15.$$ Hence, the largest area that the given parallelogram can have is 15. This implies that the correct answer is the option A.

I hope it helps you.

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arshejwal: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Sep 14, 2016 2:14 am

by arshejwal » Mon Jun 18, 2018 3:25 am

Base = 5, side opposite to base = 5
Other two parallel sides = 3
A rectangle will have maximum possible area with these dimensional constraints. Area of rect = 15
Keeping the sides unchanged to keep the perimeter constant, if you change the rectangle to any rhombus the area will always be less than 15
Hence, 20 not possible.

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Jun 19, 2018 2:32 pm

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 the maximum possible area.

Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jun 20, 2018 4:05 pm

Gmat_mission 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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[email protected]

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