Final answer:
The length of the hypotenuse X in Gabriel's right triangle with legs measuring 11 inches and 10 inches is approximately 14.87 inches, which is less than 1 foot 6 inches. We found this using the Pythagorean theorem and verifying that X meets the size constraint.
Step-by-step explanation:
The student wants to find the length of the hypotenuse X in a right triangle with legs measuring 11 inches and 10 inches. To calculate this, we use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (X) is equal to the sum of the squares of the other two sides. The formula is X² = a² + b², where a and b are the lengths of the legs.
So, the calculation would be X² = 11² + 10², which simplifies to X² = 121 + 100, and further to X² = 221. To find the length of X, we take the square root of 221, which gives us X ≈ 14.87 inches. Since Gabriel can't make the piece over 1 foot and 6 inches long, and 14.87 inches is less than 18 inches (which is equal to 1 foot and 6 inches), it's safe to say that the piece of wood X will fit the requirements.