Please help me with this question !

Question

At a certain time of day, a tree that is x meters tall casts a shadow that is x − 17 meters long. If the distance from the top of the tree to the end of the shadow is x + 8 meters, what is the height, x, of the tree?

Answer 1

When you make this sketch you have a right triangle.

 

the legs are the tree and the shadow.

 

The hypotenuse is the distance from the top of the tree to the end of the shadow.

 

you are given the lengths of the sides of all the sides so we can use Pythagorean Theorem to solve for x.

 

x^2 + (x-17)^2=(x+8)^2

 

x^2 + x^2 -34x + 289 = x^2 + 16x + 64

 

2x^2 - 34x + 289 = x^2 + 16x + 64

 

move ever thing to one side

 

x^2 - 50x + 225 = 0

 

no quadratic equation so factor 

 

(x-5) ( x-45) = 0

 

set each factor = 0

 

x-5=0 or x-45=0

 

x=5 or x=45

 

So 2 possible answers.

 

if x is 5 the tree is 5 and the shadow is negative 12...oops that is not going to work

 

if x is 45 the tree is 45, the shadow is 28, and the distance from the tree to the end of the shadow is 53.

 

That works.

 

So height of the tree is 45.

 

Let me know if you need me to explain any of that better.  :-)