The figure shows a quadrangle ABCD with

[Max@Math Revolution]

[GMAT math practice question]

The figure shows a quadrangle ABCD with ∠ADC = 90, ∠DCB = 90 and AD = 6, AB = 8 and BC = 10. What is the length BD?

A. 2 \(\sqrt{37}\)
B. 10
C. 3 \(\sqrt{39}\)
D. 14
E. 5 \(\sqrt{41}\)

[Max@Math Revolution]

=>

From the above figure, since we have EC = 6, we have BE = 4. Then we use Pythagorean Theorem to solve for AE, giving us AE = \(\sqrt{8^2-4^2}=\sqrt{64-16}=\sqrt{48}=4\sqrt{3}\) and AE = DC = 4√3.
Thus, we have x = \(\sqrt{10^2+\left(4\sqrt{3}\right)^2}=\sqrt{100+48}=2\sqrt{37}\)

Therefore, A is the answer.
Answer: A