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 22 is not equal to 15.
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.
Are you sure.....
Apologies for the confusion. Let me correct my previous response.
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 of the Pythagorean Theorem states that 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, the longest side is 15 (hypotenuse) and the other two sides are 10 and 12. Now, we can calculate:
10^2 + 12^2 = 100 + 144 = 244
Since the square of the longest side (15^2) is not equal to the sum of the squares of the other two sides (244), we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Which answer is it, though?
Apologies for the confusion earlier. The correct answer is:
No, because 244 is not equal to 225.
Since the square of the longest side (15^2) is not equal to the sum of the squares of the other two sides (244), 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 using the converse of the Pythagorean theorem, we need to 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 sides of the given triangle are 15, 10, and 12. To find the longest side, we can compare the lengths and identify that 15 is the largest.
Now, let's apply the converse of the Pythagorean theorem. We square the longest side (15) and add the squares of the other two sides (10 and 12).
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.