Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right angle
a:No, because 22 is not equal to 15
b:No, because 369 is not equal to 100
c:No, because 325 is not equal to 144
d:No, because 244 is not equal to 225
The correct answer is d: No, because 244 is not equal to 225. The Converse of the Pythagorean Theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle. In this case, the sum of the squares of the shorter sides (10 and 12) is equal to 244, which is not equal to the square of the longest side (15 squared is 225). Therefore, the triangle is not a right angle.
To determine whether a triangle with sides 15, 10, and 12 is a right angle, we need to apply 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 lengths of the other two sides, then the triangle is a right triangle.
Let's calculate the squares of the given sides:
15 squared = 225
10 squared = 100
12 squared = 144
Now we need to check if the square of the longest side (15) is equal to the sum of the squares of the other two sides (10 and 12).
225 is not equal to 100 + 144. Therefore, the triangle with sides 15, 10, and 12 is not a right angle.
So, the correct answer is:
d: No, because 244 is not equal to 225
To determine if a triangle with sides 15, 10, and 12 is a right angle triangle, we can use the Converse of the Pythagorean Theorem.
The Pythagorean Theorem states that in a right angle 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 lengths of the other two sides.
In this case, we have sides of lengths 15, 10, and 12. Let's determine if the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.
To do this, we square each side length:
15^2 = 225
10^2 = 100
12^2 = 144
Now, let's check if the square of the longest side (225) is equal to the sum of the squares of the other two sides (100 + 144):
225 = 100 + 144
225 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right angle triangle.
So, the correct answer is (d) No, because 244 is not equal to 225.