The figure below shows rectangle ABCD with AB = 6 and AO = 5. What is the circumference of ABCD?

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Feb 21, 2020 12:42 am

[GMAT math practice question]

The figure below shows rectangle ABCD with AB = 6 and AO = 5. What is the circumference of ABCD?

2.21ps.png

A. 26
B. 27
C. 28
D. 29
E. 30

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Source: Beat The GMAT — Problem Solving | Fri Feb 21, 2020 12:42 am

Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

Re: The figure below shows rectangle ABCD with AB = 6 and AO = 5. What is the circumference of ABCD?

by Max@Math Revolution » Sun Feb 23, 2020 6:11 pm

=>

We have AC = 2AO = 2*5 = 10.
Since we have AC^2 = AB^2 + BC^2, we have BC^2 = AC^2 – AB^2 = 10^2 – 6^2 = 100 – 36 = 64 or BC = 8.

Thus, the perimeter of ABCD is 2(6+8) = 2*14 = 28.

Therefore, C is the answer.
Answer: C

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