Question of the Week- 8 (In the quadrilateral shown above,........)

Question

e-GMAT          Question of the Week #8

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In the quadrilateral shown above, the length of AB and CD is 6 units and 8 units respectively. If the length of AC is 10 units, then which of the following can be the perimeter of quadrilateral ABCD?

a)  20 units
 b)  35 units
 c)  48 units
 d)  52 units
 e)  60 units

To access all the questions:     Question of the Week: Consolidated List

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EgmatQuantExpert · Accepted Answer

Solution

Given:  
  • AB= 6 units
 • CD= 8 units
 • AC= 10 units

To find:  
  • The option which can be the correct diameter of quadrilateral ABCD.

Approach and Working:

Perimeter of ABCD= AB+BC+CD+DA= 8+6+AD+BC= 14+AD+BC
  • Hence, we will get the minimum value of perimeter when AD and BC are minimum
 • And, we will get the maximum value of perimeter when AD and BC are maximum.

In ∆ ADC,
  • 10-8 < AD < 10+8
 • 2 < AD < 18

In ∆ ABC,
  • 10-6 < BC < 10+6
 • 4 < BC < 16

Hence, 6 < AD+BC < 34

Thus, 20<Perimeter of ABCD< 48

The only option which lies between 20 and 48 is 35.

Hence, the correct answer is option B.

Answer: B

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kunalcvrce · Answer

In triangle ADC , 3<AD<17 
In triangle ABC , 5<BC<15

Therefore Max perimeter 8+6+17+15=46
Min perimeter 6+8+3+5=22
  22<P<46 
So B

rahul16singh28 · Answer

The Answer has to be  B .

From the Property of Traingle (i.e. Sum of two sides is always greater than third side).

In Triangle ADC,  2 < AD < 18

In Triangle ABC,  4 < BC < 16.

Add the Max value of AD & BC + 14. Only option B satisfies.

raks85 · Answer

Given , AB = 6, CD = 8, AC = 10
Question : Perimeter = AB + BC + CD + AD = ?, i.e. BC + AC + 14 = ?
Required, value of AD and BC to find out perimeter of the quadrilateral.

For Triangle ADC :
AD < AC + DC, Hence, AD < 10+8 = 18 ---- (1)
And, AD+DC > AC, Hence, AD > 2 -----------(2)
(Checking AD + AC > DC not required as already AC> DC)

For Triangle ABC :
BC < AB+AC, Hence, BC < 6+10 = 16 -------(3)
And, AB + BC > AC, hence, BC > 4 -----------(4)
(Checking BC + AC > AB not required as already AC > AB)

From Eq. (1) & (3) we get P <48 and from Eq. (3) & (4) we get P >24.
Only (B) satisfies this. Hence, answer is (B) 35 units.

EgmatQuantExpert · Answer

Hey  kunalcvrce ,

Your answer is correct. 
But, can you please tell me, how you arrived at:
 "In triangle ADC ,3<AD<17
In triangle ABC ,5<BC<15"

It should be 2<AD<18 and 4<BC<16

Regards,
Ashutosh
e-GMAT

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kunalcvrce · Answer

Hi  EgmatQuantExpert

I missed the equal sign considering sides are integer. Thanks for correcting.

kunalcvrce · Answer

EgmatQuantExpert 
It’s a proper GMAT type question.
I will say it’s a simple and tricky question. If triangle property didn’t strike on time then this question will become most difficult to solve .

Sent from my iPhone using  GMAT Club Forum mobile app

EgmatQuantExpert · Answer

Hey  kunalcvrce ,

Thanks for your feedback. We will try our best to give the best GMAT like questions in our  Question of the Week series .

Regards,
Ashutosh
e-GMAT

EgmatQuantExpert · Answer

Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT

Shubhradeep · Answer

We have 2 equations 2<AD<18  &  4<BC<16
That means AD∈    &  BC∈

So, the highlighted part is wrong. It should be AD+BC ∈   or    8\leq{AD+BC}\leq{32}

So, perimeter is bound be between (8+14) and (32+14) i.e, perimeter ∈

Only option is this range is 35 (Option B)

Question of the Week- 8 (In the quadrilateral shown above,........)

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