The converse of the Pythagorean theorem states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
In this case, we have a triangle with sides 15, 10, and 12.
Using the converse of the Pythagorean theorem, we need to check if the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides.
Let's check for all three sides:
- For side length 15, the sum of the squares of the other two sides is 10^2 + 12^2 = 100 + 144 = 244. But 15^2 = 225. Since 244 is not equal to 225, the triangle is not a right triangle.
- For side length 10, the sum of the squares of the other two sides is 12^2 + 15^2 = 144 + 225 = 369. But 10^2 = 100. Since 369 is not equal to 100, the triangle is not a right triangle.
- For side length 12, the sum of the squares of the other two sides is 10^2 + 15^2 = 100 + 225 = 325. But 12^2 = 144. Since 325 is not equal to 144, the triangle is not a right triangle.
Therefore, based on the converse of the Pythagorean theorem, the triangle with sides 15, 10, and 12 is not a right triangle.
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
1 answer