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# help geometry

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In rectangle ABCD, shown here, CE is perpendicular to BD. If BC = 3 and DC = 3, what is CE?

Jul 11, 2021

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Answer: $$1.5\sqrt2$$

Solution:

If BC and DC are equal to each other (they are both three), then ABCD must be a square. BD would just be a diagonal of said square, splitting it in half. CE at that ponit is obviously just 1/2 of BD, and BD is $$3\sqrt2$$ ($$\sqrt(3\cdot3+3\cdot3)$$, as according to the Pythagorean theorem). Multiplying those two together gives an answer of $$1.5\sqrt2$$.

Jul 11, 2021
edited by WhyamIdoingthis  Jul 11, 2021