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In a right triangle, one leg is x, the other leg is 13, and the hypotenuse is 26. F...

Check the final answer first, then review the worked steps.

Answer

22.52 units

Step-by-step solution

  1. Identify the problem type: This is a geometry problem involving a right triangle.
  2. Recognize the relationship between sides: The image shows a right triangle with legs of length $x$ and $13$, and a hypotenuse of length $26$. The Pythagorean theorem relates the lengths of the sides of a right triangle: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.
  3. Apply the Pythagorean theorem: Substitute the given values into the theorem: $x^2 + 13^2 = 26^2$.
  4. Calculate the squares: $13^2 = 169$ and $26^2 = 676$. The equation becomes $x^2 + 169 = 676$.
  5. Isolate $x^2$: Subtract $169$ from both sides of the equation: $x^2 = 676 - 169$.
  6. Perform the subtraction: $x^2 = 507$.
  7. Solve for $x$: Take the square root of both sides: $x = \sqrt{507}$.
  8. Calculate the approximate value of $x$: Using a calculator, $\sqrt{507} \approx 22.51666$. Rounding to two decimal places, $x \approx 22.52$.