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

 

 Apr 26, 2022
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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

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