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The figure shows ABCD with AB = 8, BC = 17 and

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The figure shows ABCD with AB = 8, BC = 17 and

by Max@Math Revolution » Fri Jun 05, 2020 12:30 am

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[GMAT math practice question]

The figure shows ABCD with AB = 8, BC = 17 and CD = 9 and \(\angle\) BAC = \(\angle\) ADC = 90. What is the area of ABCD?
6.5PS.png
A. 81
B. 92
C. 103
D. 114
E. 125
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Re: The figure shows ABCD with AB = 8, BC = 17 and

by Max@Math Revolution » Sun Jun 07, 2020 6:27 pm
=>

AC^2 = 17^2 – 8^2 = (17 + 8)(17 - 8) = 25·9 = 5^2·3^2 = 15^2.
Thus, we have AC = 15.
AD^2 = AC^2 - CD^2 = 15^2 - 9^2 = (15 + 9)(15 - 9) = 24·6 = 2^2·6^2 = 12^2.
Thus, we have AD = 12.

ABCD = ABC + ACD = (1/2)·8·15 + (1/2)·12·9 = 60 + 54 = 114.

Therefore, D is the answer.
Answer: D
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