Question

Which of the following sets of sides create a right triangle?

A. 5, 7, 11
B. 5, 12, 13
C. 9, 16, 23
D. 4, 4, 7

Answer 1

Using the Pythagorean theorem, only set B (5, 12, 13) creates a right triangle as it satisfies the condition 5² + 12² = 13².

Step-by-step explanation:

To determine which set of sides creates a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). Mathematically, this can be expressed as a² + b² = c², where a and b are the legs, and c is the hypotenuse.

• For the set A (5, 7, 11), checking if 5² + 7² = 11²: 25 + 49 does not equal 121, so it's not a right triangle.
• For the set B (5, 12, 13), checking if 5² + 12² = 13²: 25 + 144 equals 169, so set B forms a right triangle.
• For the set C (9, 16, 23), checking if 9² + 16² = 23²: 81 + 256 does not equal 529, so it's not a right triangle.
• For the set D (4, 4, 7), checking if 4² + 4² = 7²: 16 + 16 does not equal 49, so it's not a right triangle.

Thus, the right triangle is formed by set B (5, 12, 13).