Final answer:
The length of the third side of the right triangle, which is the hypotenuse, is approximately 7.81 inches. The perimeter of this triangle, when adding all three side lengths, is about 18.81 inches, with the closest answer choice being 18.62 inches. These calculations are based on the Pythagorean theorem.
Step-by-step explanation:
To calculate the length of the third side which is given as √61 inches, we will approximate the square root. The value of √61 is approximately 7.81 inches. Therefore, the correct answer for the length of the third side is A) 7.81 inches.
To find the perimeter of the triangle, simply add the lengths of all three sides: 5 inches + 6 inches + 7.81 inches, which gives us about 18.81 inches. However, none of the answer choices exactly match this calculation. The closest value to this perimeter is A) 18.62 inches.
Remember, the Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c), with the formula a² + b² = c². This principle is applied to solve for the third side of a right triangle when the two other sides are known.