rohit_gmat wrote:
In the figure above (see attachment), segment BD has length 6. What is the length of segment AC?
1) The area of quadrilateral ABCD is 60.
2) The length of segment AD is 10.
OA
A
Is there any concept to be used here? Is it a parallelogram or smth?? plz help.
thanks!
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.
![Image](https://s1.postimage.org/jem21z3m3/diagonal_AC.jpg)
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.
![Image](https://s1.postimage.org/kn9xnlvkb/diagonal_AC_different_lengths.jpg)
The figures above illustrate that AC can be different lengths.
INSUFFICIENT.
The correct answer is
A.
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