Using the converse of the Pythagorean theorem explain whether a triangle with sides 15, 10, and 12 is a right triangle. No because 22 is not equal to 15, no because 369 is not equal to 100, no because 244 is not equal to 255, no because 325 is not equal to 144
The converse of the Pythagorean theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In this case, the longest side of the triangle is 15. If the triangle is a right triangle, then the sum of the squares of the other two sides should be equal to the square of the longest side.
Checking the sums of the squares of the other two sides:
- 10^2 + 12^2 = 100 + 144 = 244, which is not equal to 15^2 (225)
- 10^2 + 12^2 = 100 + 144 = 244, which is not equal to 15^2 (225)
- 10^2 + 15^2 = 100 + 225 = 325, which is not equal to 12^2 (144)
Since none of the sums of the squares of the other two sides are equal to the square of the longest side, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
To determine if a triangle with sides 15, 10, and 12 is a right triangle, we can use the converse of the Pythagorean theorem. According to the converse, if the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Let's calculate:
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
15^2 ≠ 10^2 + 12^2
Since 225 is not equal to 244, we can conclude that the given triangle with sides 15, 10, and 12 is not a right triangle.
To determine whether a triangle is a right triangle using the converse of the Pythagorean theorem, we check if the square of the longest side is equal to the sum of the squares of the other two sides.
In this case, the longest side is 15. We need to check if the sum of the squares of the other two sides, 10 and 12, equals 15^2.
Calculating the squares:
10^2 = 100
12^2 = 144
Now, we compare the sum of these squares (100 + 144 = 244) with the square of the longest side (15^2 = 225).
Since the sum of the squares of the other two sides is not equal to the square of the longest side (244 ≠ 225), we can conclude that the triangle with side lengths 15, 10, and 12 is not a right triangle.
Therefore, the answer is "No, because 244 is not equal to 225."