Question

Which of the following sets of numbers could not represent the three sides of a right

triangle?
{20, 48,52}
{40, 75, 85}
{14, 47,50}
{13, 84, 85}

Answer 1

{14, 47, 50}

Explanation:

The three sides of a right triangle must satisfy

a² + b² = c², known as the Pythagorean Theorem. So let's put the pairs into the theorem.

20, 48, 52

a² + b² = c²

20² + 48² = 52²

400 + 2304 = 2704

2704 = 2704

20, 48, and 52 represent the three sides of a right triangle.

40, 75, 85

a² + b² = c²

40² + 75² = 85²

1600 + 5625 = 7225

7225 = 7225

40, 75, and 85 represent the three sides of a right triangle.

14, 47, 50

a² + b² = c²

14² + 47² = 50²

196 + 2209 = 2500

2405 ≠ 2500

14, 47, and 50 do NOT represent the three sides of a right triangle.

13, 84, 85

a² + b² = c²

13² + 84² = 85²

169 + 7056 = 7225

7225 = 7225

13, 84, and 85 represent the sides of a right triangle.

14, 47, and 50 do NOT represent the three sides of a right triangle, therefore making it your answer.