### Instruction: For $x > 0$, the area of the triangle with vertices $(0, 0), (x, 2x)$, and $(x, 0)$ is 64 square units. What is the value of $x$?### Response: I notice that this triangle is a right triangle with a horizontal leg of length x and a vertical leg of length 2x.
The area of a right triangle is half the product of the lengths of the legs, so I can write an equation:
Area = (1/2) * x * 2x = 64
Simplifying, I get:
x^2 = 64
Taking the square root of both sides, I get:
x = ± 8