Pythagorean Theorem

Question

(1 point) A tree is supported by a wire anchored in the ground 6 feet from its base. The wire is 5 feet longer than the height that it reaches on the tree. How long is the wire?
a) Use the Pythagorean theorem to write a polynomial equation to solve to answer the question. Use the variable x
to represent the length of the wire .
Answer: 

b) Solve the equation and give the length of the wire. Use feet for units.
Answer: 

Answer 1

It is helpful to draw a diagram in these types of problems. The tree can represent the vertical leg of the triangle. The distance from the base of the tree to the spot where the wire is anchored represents the horizontal leg of the triangle. The length of the wire will be the hypotenuse of the right triangle. If the length of the wire is x, then the height it reaches on the tree is (x - 5) since the length of the wire is 5 ft longer than the height it reaches on the tree. Using the Pythagorean Theorem yields:

 

(x - 5)² + 6² = x²

(x - 5)² + 36 = x²

 

Solve this equation for x to determine the length of the wire.