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At a certain time of day, a tree that is x meters tall casts a shadow that is x−21 meters long. If the distance from the top of the tree to the end of the shadow is x+3 meters, what is the height, x, of the tree?

 Aug 11, 2021
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\(x^2 + (x-21)^2 = (x+3)^2\)

\(x^2 + x^2 + 441 - 42x = x^2 + 9 + 6x\)

\(x^2 - 48x + 432 = 0\)

Use quadratic formula: \(x = {48 \pm \sqrt{(-48)^2-4*1*432} \over 2}\)

\(48 \pm 24 \over 2 \)

x = 12, 36

But, shadows can't be negative so the answer is 36.

 Aug 11, 2021

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