Which of the following sets of numbers could not represent the three sides of a right triangle?
{48,55,73}
left curly bracket, 42, comma, 56, comma, 70, right curly bracket{42,56,70}
left curly bracket, 39, comma, 80, comma, 89, right curly bracket{39,80,89}
left curly bracket, 10, comma, 23, comma, 26, right curly bracket{10,23,26}
To determine if a set of numbers could represent the sides of a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle with sides of lengths a, b, and c (where c is the hypotenuse), the equation a^2 + b^2 = c^2 must hold.
Let's check each set of numbers:
{48, 55, 73}
48^2 + 55^2 = 2304 + 3025 = 5329
73^2 = 5329
Since 48^2 + 55^2 = 73^2, this set of numbers can represent the sides of a right triangle.
{42, 56, 70}
42^2 + 56^2 = 1764 + 3136 = 4900
70^2 = 4900
Since 42^2 + 56^2 = 70^2, this set of numbers can represent the sides of a right triangle.
{39, 80, 89}
39^2 + 80^2 = 1521 + 6400 = 7921
89^2 = 7921
Since 39^2 + 80^2 = 89^2, this set of numbers can represent the sides of a right triangle.
{10, 23, 26}
10^2 + 23^2 = 100 + 529 = 629
26^2 = 676
Since 10^2 + 23^2 ≠ 26^2, this set of numbers cannot represent the sides of a right triangle.
Therefore, the set {10, 23, 26} could not represent the three sides of a right triangle.