SOLUTION: 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 long

Question 1156068: 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 long, what is the height, "x", of the tree?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Consider as a right triangle with hypotenuse (x+3), and square is x^2+6x+9
one leg is (x-21) the shadow--square is x^2-42x+441
the height is and square is x^2
The last two equal the first
2x^2-42x+441=x^2+6x+9
x^2-48x+432=0
(x-36)(x-12)=0
x=36 and x=12. The latter doesn't work, because x-21 is negative.
The tree is 36 feet tall ANSWER
36^2+15^2=39^2, which is a multiple of 3 of a 5-12-13 right triangle.
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