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

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Source: — Data Sufficiency |
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by nitink » Tue Dec 03, 2019 11:01 am
We need to know all the sides of the trapezium to find the perimeter.

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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