Question

Which of the following sets could be the sides of a right triangle?

a) (2, 3, 10)
b) (3, 5, 134)
c) {5, 8, 12}
d) None of the above

Answer 1

To determine if a set of sides can be a right triangle, we need to see if it satisfies the Pythagorean theorem. Only the set {5, 8, 12} satisfies the theorem and can be the sides of a right triangle. Hence the correct answer is option C

Step-by-step explanation:

To determine which sets could be the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's check each set:

a) (2, 3, 10): 2^2 + 3^2 = 4 + 9 = 13 > 10^2 = 100. Not a right triangle.

b) (3, 5, 134): 3^2 + 5^2 = 9 + 25 = 34 < 134^2 = 17956. Not a right triangle.

c) {5, 8, 12}: 5^2 + 8^2 = 25 + 64 = 89 = 12^2 = 144. This is a right triangle.

d) None of the above: This choice is incorrect because c) {5, 8, 12} is a set that satisfies the Pythagorean theorem and can be the sides of a right triangle.