Answer:
x = 3√7
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, the sum of the legs squared and added together is equal to the hypotenuse (the longest side and the one across the 90° angle)
If the legs are a and b, respectfully, and the hypotenuse is c, the equation would be:
a² + b² = c²
Let's apply this to the problem given.
9² + x² = 12²
Simplify.
81 + x² = 144
Subtract 81 from both sides.
x² = 63
Take the square root.
√(x²) = √63 = √(9 * 7) = √(3² * 7)
x = 3√7
Check the answer.
9² + (3√7)² = 12²
81 + 9 * 7 = 144
81 + 63 = 144
144 = 144
Thus, the answer is correct.
I hope this helps! Feel free to ask any questions! :)