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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Dec 02, 2019 8:22 pm

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

(1) AB = 10

(2) AD = 6

OA C

Source: Magoosh

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 02, 2019 8:22 pm

nitink: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Thu Oct 11, 2018 9:10 am

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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