 It is currently 26 Mar 2019, 00:38 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A quadrilateral has a perimeter of 16. Which of the followin  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Senior Manager Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50  , given: 220

A quadrilateral has a perimeter of 16. Which of the followin [#permalink]
1
KUDOS 00:00

Question Stats: 4% (00:36) correct 95% (01:15) wrong based on 21 sessions
A quadrilateral has a perimeter of 16. Which of the following alone would provide sufficient information to determine the area of the quadrilateral. Choose ALL that apply.

[A] The quadrilateral contains equal sides

[B] The quadrilateral is formed by combining two isosceles right triangles

[C] Two pairs of congruent angles are in a 2:1 ratio

[D] The width is 4o% of the length and all angles are of equal measure

[E] If the perimeter was decreased by 50%, the area would decrease by 25%

Kudos for correct solution.
[Reveal] Spoiler: OA Intern Joined: 23 Mar 2018
Posts: 7
Followers: 0

Kudos [?]: 3  , given: 13

Re: A quadrilateral has a perimeter of 16. Which of the followin [#permalink]
1
KUDOS
Can someone provide the explanation for this please? Director  Joined: 07 Jan 2018
Posts: 604
Followers: 7

Kudos [?]: 546  , given: 88

Re: A quadrilateral has a perimeter of 16. Which of the followin [#permalink]
2
KUDOS
Let us start with $$A$$
The quadrilateral has equal sides so general perception could be that this is a square however there is one more quadrilateral that has all four sides equal to one another but has an area different from square i.e Rhombus. area of square = side$$^2$$ and area of rhombus = $$1/2 D1 * D2$$ so a is not true
$$B$$
The quadrilateral contains two right angled triangle hence there are two $$45-45-90$$ triangle as such all four sides of the quadrilateral should be equal but this does not necessarily mean the quadrilateral is a square as it could again be a rhombus

$$C$$
In this case we can be certain that the quadrilateral is not a square as all the angles of square are $$90$$ degrees. This could be a parallelogram however there could be multiple scenarios for a perimeter of $$16$$ for eg. a side of $$6$$ and $$2$$ or $$7$$ and $$1$$ or $$5$$ and $$3$$ with a $$2:1$$ ratio of ($$60,120$$) degrees
In all of these variation in sides area will be different also notice that we need a height to get the area of a parellelogram which is not given nor can be derived hence c is also false

$$D$$
For a quadrialteral all angles add to $$360$$ degrees hence if all angles are equal $$4x =360$$and as such each angle $$(x)$$ = $$90$$ degrees furthermore given that width is $$0.4$$ of length the quadrilateral is not a square or rhombus but a rectangle
we can find the exact length and width of the rectangle $$2(l + 0.4l) = 16$$
or $$1.4 l = 8$$
therefore $$l = 5.70$$ approx
similarly we can get the width $$= 2.28$$
and area = $$12.996$$
hence $$D$$ is true

$$E$$
Let us take a rectangle with sides $$6$$and$$2$$
Initial perimeter = $$16$$
50% decrease in perimeter so new perimeter = $$8$$
This should bring about $$25$$% reduction in area
original are
a = $$6*2 =12$$
new area = $$12*0.75 = 9$$

However a combination of length and breadth with perimeter $$16$$ for a rectangle can be many such as $$7,1$$; $$5,3$$
In each case the area is not same and hence when the perimeter and area is reduced by 50% and 25% respectively we get a different area for different set of sides

for $$7,1$$ original area = $$7$$ after reduction = $$5.25$$
for $$5,3$$ original area = $$15$$ after reduction = $$11.25$$
We cannot be sure of the area hence E is also false
only D
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes Re: A quadrilateral has a perimeter of 16. Which of the followin   [#permalink] 27 Apr 2018, 00:16
Display posts from previous: Sort by

# A quadrilateral has a perimeter of 16. Which of the followin  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.