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 325 is not equal to 144.
No, because 325 is not equal to 144.
No, because 244 is not equal to 225.
No, because 244 is not equal to 225.
No, because 369 is not equal to 100.
No, because 369 is not equal to 100.
No, because 22 is not equal to 15.
No, because 22 is not equal to 15.
To determine whether a triangle is a right triangle using the converse of the Pythagorean Theorem, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
In this case, the longest side is 15.
Calculating the squares of the shorter sides:
10^2 = 100
12^2 = 144
The sum of the squares of the shorter sides is:
100 + 144 = 244
Since 244 is not equal to 225 (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 whether a triangle is a right triangle, we can use the Converse of the Pythagorean Theorem. According to the Converse of the Pythagorean Theorem, if the square of the length 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, we have a triangle with sides measuring 15, 10, and 12. To check if it is a right triangle, we need to calculate the squares of these side lengths and see if the longest side's square is equal to the sum of the squares of the other two sides.
The longest side in this case is 15. Let's calculate the squares of the other two sides:
10^2 = 100
12^2 = 144
Now, let's check if the square of the longest side, 15^2, is equal to the sum of the squares of the other two sides, 100 + 144.
15^2 = 225
100 + 144 = 244
Since 225 is not equal to 244, we can conclude that the triangle with sides measuring 15, 10, and 12 is not a right triangle.