The Converse of the Pythagorean Theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle. The sides given are 15, 10, and 12.
Let's test whether any of these sides can be the hypotenuse of a right triangle by applying the Pythagorean Theorem:
The sum of the squares of the two shorter sides (10 and 12) should equal the square of the hypotenuse (if it's a right triangle). So we will check if 10^2 + 12^2 = 15^2:
10^2 = 100
12^2 = 144
15^2 = 225
Now, we add the squares of the two shorter sides:
100 + 144 = 244
Next, we compare this sum to the square of the longest side (hypotenuse):
244 ≠ 225
Since 244 is not equal to 225, the sides 15, 10, and 12 do not meet the condition stated in the Converse of the Pythagorean Theorem for a right triangle.
Therefore, the correct answer is:
C: No, because 244 is not equal to 225.
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A: No, because 325 is not equal to 144.
B: No, because 22 is not equal to 15.
C: No, because 244 is not equal to 225.
D: No, because 369 is not equal to 100.
1 answer
1 answer