Final answer:
Calculating the perimeter of each triangle formed by cutting a rectangle diagonally, we use the Pythagorean theorem to find the hypotenuse. The perimeter sum (16 inches + 30 inches + 34 inches) is 80 inches, not matching any of the provided options.
Step-by-step explanation:
Clarence cuts a 16-inch by 30-inch piece of plywood diagonally to create two right-angled triangles. Each triangle will have sides of 16 inches, 30 inches, and the hypotenuse which is the diagonal of the rectangle.
To find the length of the diagonal, we can apply the Pythagorean theorem (a² + b² = c²) where the diagonal (c) is the hypotenuse of each triangle, and the sides of the rectangle (a and b) are 16 and 30 inches respectively. Hence, c = √(16² + 30²) = √(256 + 900) = √1156 = 34 inches.
The perimeter of each triangle is the sum of its three sides: Perimeter = a + b + c, which equates to 16 + 30 + 34 = 80 inches. However, this option isn't listed in the multiple choices given, indicating a potential error in the question or choices provided. It is possible to round the hypotenuse to the nearest inch if approximation is acceptable, resulting in a hypotenuse of approximately 33 inches and a perimeter of 79 inches. Nevertheless, even after rounding, the answer does not clearly match any of the given options, suggesting that none of the provided options are correct.