Question

At a certain time of day, a tree that is x meters tall casts a shadow that is x−46x−46 meters long. if the distance from the top of the tree to the end of the shadow is x+4x+4 meters long, what is the height, x, of the tree?

Answer 1

By the Pythagorean theorem,
.. x^2 +(x -46)^2 = (x +4)^2
.. 2x^2 -92x +2116 = x^2 +8x +16
.. x^2 -100x +2100 = 0
.. (x -50)^2 -400 = 0
.. x = 50 ±20 . . . . . only x=70 makes any sense in the problem

The height, x, of the tree is 70 meters.