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# geometry

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In rectangle ABCD, corner A is folded over crease DE to point F on BC.  Find BC.

Apr 26, 2022

#1
+1370
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We know that $$EF = 9$$

Using the Pythagorean Theorem, $$BF = \sqrt{45}$$

Let $$DF = BC = x$$

We can derive the following equation using the Pythagorean Theorem: $$x^2=225+(x-\sqrt{45})^2$$

Solving, we find that $$\color{brown}\boxed{BC = 3 \sqrt{45}}$$

Apr 27, 2022