Algebra 2 Word problem

Question

The lengths of the sides of a right triangle are x, (x+3), and (x+6) inches. 

 

1. What is the value of x?

 

2. What is the length of the hypotenuse of the triangle?  

Answer 1

A. x² + (x + 3)² = (x + 6)²

 

How do we know which is the hypotenuse? It's the longest.

 

x² + x² + 6x + 9 = x² + 12x + 36

x² - 6x - 27 = 0

(x - 9)(x + 3) = 0

 

In order for the left side to equal 0, either x - 9 or x + 3 has to equal 0, right?

 

x - 9 = 0

x = 9

 

x + 3 = 0

x = -3

If we were just solving for x, this would be an answer, but distance is not negative.

 

B. 9 + 6 = 15