What it the length?

Question

A tree is supported by a wire anchored in the ground 24 feet from its base. The wire is 18 feet longer than the height that it reaches on the tree. What is The length of the wire?

Answer 1

This looks like a problem that deals specifically with triangles.  The distance between the wire on the ground and the base of the tree is the horizontal distance.  The height of the wire from its base to the tree is the vertical distance.  Then length of the wire is the diagonal distance from the ground to the height.  When you draw this diagram based on the description, we get a right triangle.

 

 

Let the actual wire length = x + 18

Let the height of the wire that reaches on the tree = x

Let the distance between the ground and the base of tree = 24

 

A right triangle means that we can use the Pythagorean theorem.  Set up an equation using the theorem and variables.

 

24² + x² = (x + 18)²

 

576 + x² = x² + 36x + 324

 

 

Subtract x² on both sides of the equation.

 

576 = 36x + 324

 

 

Subtract 324 on both sides of the equation.

 

252 = 36x

 

 

Divide both sides of the equation by 36.

 

7 = x

 

 

Actual wire = 7 + 18 = 25 feet