Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle. (1 po 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.
how wrong you are!
10^2 + 12^2 ≠ 15^2
sheesh!
Apologies for the mistake. You are correct. The sum of the squares of the two shorter sides (10^2 and 12^2) is not equal to the square of the longest side (15^2). Therefore, the triangle with sides 15, 10, and 12 is not a right triangle. Thank you for pointing out the error.
To determine if a triangle 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 one 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's a right triangle, we need to see if the square of the longest side is equal to the sum of the squares of the other two sides.
First, let's find the longest side of the triangle. Comparing the three given side lengths, we can see that 15 is the largest. Now, we'll square the longest side (15^2) and find the sum of the squares of the other two sides (10^2 + 12^2).
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 244 is not equal to 225, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle. Therefore, the correct explanation is: No, because 244 is not equal to 225.