A parallelogram has perimeter 16 and base of length 5.

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

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

A parallelogram has perimeter 16 and base of length 5.

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

Timer

00:00

Your Answer

Global Stats

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.

Quote

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 pm; Thanked: 6 times; Followed by:5 members

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.

Quote

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.

Quote

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed 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!

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]