Pre-algebra
which set represents a pythagorean triple?
a. 60,70,100
b. 18,24,30
c. 10,14,17
d. 10,20,30
To determine which set represents a Pythagorean triple, we need to apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's evaluate each option:
a. 60, 70, 100: To check if this is a Pythagorean triple, we calculate: 60² + 70² = 3600 + 4900 = 8500 and 100² = 10000. These values are not equal, so option a is not a Pythagorean triple.
b. 18, 24, 30: To verify, we calculate: 18² + 24² = 324 + 576 = 900 and 30² = 900. These values are equal, so option b is a Pythagorean triple.
c. 10, 14, 17: To check, we calculate: 10² + 14² = 100 + 196 = 296 and 17² = 289. These values are not equal, so option c is not a Pythagorean triple.
d. 10, 20, 30: To verify, we calculate: 10² + 20² = 100 + 400 = 500 and 30² = 900. These values are not equal, so option d is not a Pythagorean triple.
Therefore, the only set that represents a Pythagorean triple is b. 18, 24, 30.
a^2 + b^2 = c^2
Insert values to see which fits.