In the trapezoid ABCD above, BC = 20, and AE = 8. What is the perimete

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Competition Mode Question https://gmatclub.com/forum/download/file.php?id=55887 In the trapezoid ABCD above, BC = 20, and AE = 8. What is the perimeter of ABCD? (1) AB = 10 (2) AD = 6 Are You Up For the Challenge: 700 Level Questions 1.PNG

unraveled · Answer

In the trapezoid ABCD above, BC = 20, and AE = 8. What is the perimeter of ABCD?

(1) AB = 10
Even after that point D is not fixed, giving us a variable length of perimeter ABCD. Refer first figure.

INSUFFICIENT.

(2) AD = 6
Area of Trapezium ABCD = 1/2*(6+20)*8 = 104.
The sides AB and CD are not fixed, giving us various possibilities of their lengths which vary according to area as shown in two figures.

INSUFFICIENT.

Together 1 and 2.
Total Area = 104
Only one value of length of CD is possible. Refer last figure.

SUFFICIENT.

Attachment:

Trapeziod ABCD.png [ 122.53 KiB | Viewed 5125 times ]

Note: Text in blue reflects area of respective section.

Answer C.

exc4libur · Answer

(1) insufic

using pythagoras,
we can find BE, but no info AD or DC

(2) insufic

we cannot find the other sides

(1/2) sufic

ABE is right triangle, we can find each side;
AD gives us the other sides

Ans (C)

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • In the given trapezoid ABCD, 
 o BC = 20
o AE = 8 
• We need to find the perimeter of ABCD.
 o Now, perimeter of ABCD = AB + BC + CD + DA = AB+ 20+CD + DA  
So we need to find AB, CD, and DA.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  AB = 10
 • According to this statement: AB = 10
 o  ⟹ BE = \sqrt{AB^2 – AE^2} = \sqrt{10^2 – 8^2} = 6  
• However, with the above information we cannot find AD and CD and hence we cannot find the perimeter. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  AD = 6
 • According to this statement:  AD = 6 
• However, we don’t know AB and CD. So, we cannot find the perimeter. 
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
From statement 1:
 • AB = 10 and BE = 6 
From statement 2:
 • AD = 6 
On Combining both statements:
 • Let’s drop a perpendicular DF, from D to side F, as shown in below diagram.
 o So, DF = AE = 8 
  https://www.dropbox.com/s/1q7aqgpmcipxoup/10_07_trap.jpg?dl=1

• From the above diagram, we have, CF = BC – (BE+EF) = 20 – 12 = 8
• Now, in triangle, CDF, 
 o  CD = \sqrt{DF^2 + CF^2 }= \sqrt{8^2 + 8^2 }=8\sqrt{2}  
• Since we know all sides of the trapezoid ABCD, so we can easily find the perimeter of it. 
Thus, the correct answer is  Option C.

v12345 · Answer

Statement 1: Insufficient 
In triangle ABE,
By Pythagoras theorem , BE = 6. so ,EC = 20 - 6 =14
But we still don't know the length of AD and CD , so cant find the perimeter.
 Statement 2: Insufficient 
We don't know the length of AB and CD.
Can't find the perimeter
 On combining ,
We can get all sides of trapezium ABCD and its perimeter.

Hence, OA is (C).

minustark · Answer

From all given information, we can find the length of three sides of the trapezoid. But the rightmost side will still be unknown as we don't know the ratio of angles DCB and ADC to apply the Pythagorean theorem. For perimeter of a trapezoid, length of all 4 sides need to be known.
E is the answer.

Goviz · Answer

In the given figure, it is not mentioned if the Trapezoid is isosceles or not.In that case the only information available with us is that AD||BC,BC=20 and AE=8(height of the trapezium).Draw an imaginary perpendicular from D to BC->DF is perpendicular to BC and DF is 8 
1. with this info AB=10, we can find out BE(Pythagorus theorem on triangle ABE, we get BE=6) and EC. but AD and DC cannot be solved for. Not sufficient
2. With this info AD=6, . But with info all we cannot figure out the answer. 
Using both the info 1 and 2 we can figure out all the sides as follows
AB=with 1 point , AD=with 2 point, BC=given and DC=(apply pythagorus theorem on rt angel triangle DFC, where DF=8 and FC=BC-(BF)=8

Therefore option C

debjit1990 · Answer

From 1, in triangle ABE,
By Pythagoras theorem , BE = 6. so ,EC = 20 - 6 =14
But we still don't know the length of AD and CD , so cant find the perimeter.

from 2, we still dont know the length of AB and CD.
So, cant find the perimeter.

From 1 and 2, we know the length of three sides and we can know CD by using the
area of trapezium formula. Lets drop a perpendicular from D to BC and call it as DP.

Area of trapezium ABCD = area triangle ABE + Area triangle DPC + Area rectangle AEPD.
Solve for CD.

Hence , answer is C.

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In the trapezoid ABCD above, BC = 20, and AE = 8. What is the perimete

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