Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
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 of the triangle is 15. To determine if the triangle is a right triangle, we need to calculate the squares of the other two sides (10 and 12) and sum them up:
10^2 + 12^2 = 100 + 144 = 244
Now we compare this sum with the square of the longest side:
15^2 = 225
Since the sum of the squares of the other two sides (244) is greater than the square of the longest side (225), we can conclude that the triangle is not a right triangle based on the Converse of the Pythagorean Theorem.
The Converse of the Pythagorean Theorem states that if the square of the length of the longest side 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. Let's check if the sum of the squares of the other two sides, 10 and 12, is equal to the square of 15.
10^2 + 12^2 = 100 + 144 = 244
15^2 = 225
Since 244 is not equal to 225, the triangle with sides 15, 10, and 12 is not a right triangle.
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 square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
However, the converse of the Pythagorean theorem says that if the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
In this case, we need to find the square of each side length. The square of 15 is 225, the square of 10 is 100, and the square of 12 is 144.
Next, we need to check if the sum of the squares of the two smaller sides is equal to the square of the longest side.
100 + 144 = 244
Since the sum of the squares of 10 and 12 is not equal to the square of 15, which is 225, the triangle with sides of lengths 15, 10, and 12 is not a right triangle.