A right triangle has one leg with a length of 8 units and a hypotenuse with a length of 17 units. What is the perimeter…

The correct answer is 40. The Pythagorean theorem states that for a right triangle with legs of length a and b and a hypotenuse of length c, a² + b² = c^2. In this problem, one leg is 8 and the hypotenuse is 17. Let the length of the other leg be b.

So, 8² + b² = 17^2. This gives 64 + b² = 289. Subtracting 64 from both sides gives b² = 225. Taking the square root of both sides gives b = 15. The perimeter of the triangle is the sum of the lengths of its three sides: 8 + 15 + 17 = 40.

A is incorrect because 15 is the length of the second leg, not the perimeter.

B is incorrect because 25 is the sum of the two given side lengths (8 + 17), but this omits the third side.

D is incorrect because 60 is the area of the triangle (0.5 · 8 * 15), not the perimeter.