Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
1. No, because 325 is not equal to 144.
2. No, because 244 is not equal to 225
3. No, because 369 is not equal to 100
4. No, because 22 is not equal to 15
The correct answer is 3. No, because 369 is not equal to 100. According to the Converse of the Pythagorean Theorem, if the sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle. In this case, the sum of the squares of 10 and 12 is 244, which is not equal to the square of 15 (225). Therefore, the triangle with sides 15, 10, and 12 is not a right triangle.
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.
To apply this, we need to square the lengths of the sides and check if they satisfy the equation 15^2 + 10^2 = 12^2.
Simplifying the equation, we have:
225 + 100 = 144
325 = 144
Since 325 is not equal to 144, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Therefore, option 1 "No, because 325 is not equal to 144" is correct.
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 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.
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, we can check if the sum of the squares of the two shorter sides (10^2 + 12^2 = 100 + 144 = 244) is equal to the square of the longest side (15^2 = 225).
From the options you provided, the statement "No, because 244 is not equal to 225" is the correct explanation. Since the sum of the squares of the two shorter sides is not equal to the square of the longest side, the triangle with sides 15, 10, and 12 is not a right triangle according to the Converse of the Pythagorean Theorem.