Question

Use the Pythagorean Theorem to find the unknown lengths
2X+2
3X-2
X

Answer 1

The Pythagorean Theorem relates the lengths of the legs of a right triangle to the length of the hypotenuse. Substitute the given lengths into the equation and solve for x.

Step-by-step explanation:

The Pythagorean Theorem relates the lengths of the legs of a right triangle to the length of the hypotenuse. It states that a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse. In this case, the lengths are given as 2x + 2, 3x - 2, and x. Substitute these values into the equation to solve for x.

1. Substitute the given lengths into the Pythagorean Theorem: (2x + 2)² + (3x - 2)² = x².
2. Simplify the equation: 4x² + 8x + 4 + 9x² - 12x + 4 = x².
3. Combine like terms: 13x² - 4x + 8 = x².
4. Move all terms to one side: 13x² - x² - 4x + 8 = 0.
5. Combine like terms: 12x² - 4x + 8 = 0.
6. Factor the equation: 4(3x² - x + 2) = 0.
7. Apply the zero product property and solve for x: 3x² - x + 2 = 0.
8. Use factoring, quadratic formula, or completing the square to solve for x.