Question

A set of three positive integers a, b and c that form the sides of a right triangle. For example: 3, 4, and 5.

A) 1, 3, 4
B) 2, 3, 5
C) 3, 5, 6
D) 5, 7, 8

Answer 1

The Pythagorean theorem relates the length of the legs of a right triangle with the hypotenuse. To find a set of three positive integers that form the sides of a right triangle, substitute the given values into the equation and solve for c. The correct set of positive integers is 5, 7, 8. Hence the correct answer is option D

Step-by-step explanation:

The Pythagorean Theorem

The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². This can be rewritten, solving for c: c = √(a² + b²).

Applying the Theorem

To find a set of three positive integers that form the sides of a right triangle, we can substitute the given values of a and b into the equation and solve for c.

• A) 1, 3, 4: 1² + 3² = 10 ≠ 4² (not a right triangle)
• B) 2, 3, 5: 2² + 3² = 13 ≠ 5² (not a right triangle)
• C) 3, 5, 6: 3² + 5² = 34 ≠ 6² (not a right triangle)
• D) 5, 7, 8: 5² + 7² = 74 = 8² (a right triangle)

Therefore, the correct set of positive integers that form the sides of a right triangle is D) 5, 7, 8.