Can you find the area of the following square given the known lengths?
Good luck!
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asked Sep 17, 2019 at 1:29
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$\begingroup$ just checking: did you make this yourself? $\endgroup$– Omega KryptonCommented Sep 17, 2019 at 1:50
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1$\begingroup$ No. I've been sent this problem by a friend, but I do not have the original source. $\endgroup$– Dmitry KamenetskyCommented Sep 17, 2019 at 1:51
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$\begingroup$ This is a classic puzzle. $\endgroup$– greenturtle3141Commented Sep 17, 2019 at 3:52
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1 Answer
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The diagonal of the square is
$\sqrt{(9+3)^2+5^2} = \sqrt{169} = 13$
so the area of the square is
$(\frac{13}{\sqrt{2}})^2 = \frac{169}{2}$
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$\begingroup$ OMG that is so brilliant! No mucking around with trigonometry and simultaneous equations with multiple unknowns. THANK YOU! $\endgroup$ Commented Sep 17, 2019 at 2:15
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