Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
Responses
No, because 22 is not equal to 15.
No, because 244 is not equal to 225.
No, because 369 is not equal to 100.
No, because 325 is not equal to 144.
No, because 325 is not equal to 144.
To determine whether a triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. The Converse states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
Calculating the sum of the squares of the two shorter sides:
15^2 + 10^2 = 225 + 100 = 325
Calculating the square of the longest side:
12^2 = 144
Since 325 is not equal to 144, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle. Therefore, the correct response is:
No, because 325 is not equal to 144.
To determine if a triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.
To check if the given triangle is a right triangle, we need to calculate the squares of all sides and see if any of them satisfy the equation.
For the given triangle with sides 15, 10, and 12, we have:
15² = 225
10² = 100
12² = 144
Now, let's see if these values satisfy the equation from the Pythagorean Theorem:
225 + 100 is not equal to 144. Therefore, the given triangle is not a right triangle.
So, the correct response is: No, because 325 is not equal to 144.