What is the height of the tree? It's shadow is x-49 meters long. Distance from top of tree to shadow is x+1 meters long.

Question

At a certain time of day, a tree that is x meters tall casts a shadow that is x − 14 meters long. If the distance from the top of the tree to the end of the shadow is x + 2 meters long, what is the height, x, of the tree?

Answer 1

First, may I point out that your second sentence of the title to your submission should begin with ITS (no apostrophe); only use IT'S as a contraction meaning 'it is.'  But it describes an unsolvable problem.

 

Now let's look at the body of your submission:

At a certain time of day, a tree that is x meters tall casts a shadow that is x − 14 meters long. If the distance from the top of the tree to the end of the shadow is x + 2 meters long, what is the height, x, of the tree?"

 

This represents a right triangle with vertical legs x (tree height), horizontal leg (x-14), and hypotenuse (x+2).

Using the Pythagorean theorem, and correctly squaring the binomials involved, you should arrive at a quadratic that has two  positive integer solutions.  But only one will be meaningful (the other is 'extraneous').