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Algebra

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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