Geometery DS Q.. i jus dun get it
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- rohit_gmat
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- Amiable Scholar
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No this is not parallelogram but definitely a trapezium as angle ABD = angle BDC
so line AB || DC
Now here
AC^2= BD ^2 + (Projection of AC over DC ) ^2
NOW Project of AC over DC = DC + AB (its visible from figure)
so we have BD , We just need sum of AB and DC here
now looking over first statement
area of quadilateral = 60
or
1/2*AB*BD + 1/2*BD*DC = 60
BD*(AB + DC )=120
Which gives us value of AB + DC so 1 is alone sufficient
now looking over second statement
AD = 10
only can give us the value of AB (using pytha theorem )alone no info about DC
so statement 2 is not alone sufficient .
so line AB || DC
Now here
AC^2= BD ^2 + (Projection of AC over DC ) ^2
NOW Project of AC over DC = DC + AB (its visible from figure)
so we have BD , We just need sum of AB and DC here
now looking over first statement
area of quadilateral = 60
or
1/2*AB*BD + 1/2*BD*DC = 60
BD*(AB + DC )=120
Which gives us value of AB + DC so 1 is alone sufficient
now looking over second statement
AD = 10
only can give us the value of AB (using pytha theorem )alone no info about DC
so statement 2 is not alone sufficient .
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I solved it this way....
from the question stem : we can derive that (AB+DC)^2 + 6^2 = AC^2 ....
( I got this eq by drawing an imaginary line down from A to say point Z. Then we can say that length ZC= AB+DC ... and we know that AZ=6=BD )
Statement 1 -> area = 60 = (1/2*DC*6)+ (1/2*AB*6) = 60 ----> AB+DC= 20 --> SUFF
Statement 2 -> AD =10 .. from this we can find out AB.. but still we dont know DC.. so INSUFF..
Answer is A.
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Since both AB and CD are perpendicular to BD, AB is parallel to CD.
Thus, ABCD is a trapezoid whose bases are AB and CD and whose height is BD=6.
Area of a trapezoid = (b1 + b2)/2 * h.
Thus, area of ABCD = (AB+CD)/2 * 6 = 3(AB+CD).
Statement 1: The area of quadrilateral ABCD is 60.
Thus:
3(AB+CD) = 60
AB+CD = 20.
In the figure above, since AE is perpendicular to CE, quadrilateral ABDE is a rectangle and ∆ACE is a right triangle:
In rectangle ABDE, AE=BD=6 and DE=AB.
Thus, in ∆ACE, CE = AB+CD = 20.
Since ∆ACE is a right triangle, 6² + 20² = AC².
Thus, the length of AC can be determined.
SUFFICIENT.
Statement 2: The length of segment AD is 10.
The figures above illustrate that AC can be different lengths.
INSUFFICIENT.
The correct answer is A.
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how can we say this is a trapezoid?Since both AB and CD are perpendicular to BD, AB is parallel to CD.
Thus, ABCD is a trapezoid whose bases are AB and CD and whose height is BD=6.
Area of a trapezoid = (b1 + b2)/2 * h.
Thus, area of ABCD = (AB+CD)/2 * 6 = 3(AB+CD)
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A trapezoid is a quadrilateral with at least 2 parallel sides.factor26 wrote:how can we say this is a trapezoid?Since both AB and CD are perpendicular to BD, AB is parallel to CD.
Thus, ABCD is a trapezoid whose bases are AB and CD and whose height is BD=6.
Area of a trapezoid = (b1 + b2)/2 * h.
Thus, area of ABCD = (AB+CD)/2 * 6 = 3(AB+CD)
Since AB || CD, ABCD is a trapezoid.
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