Pythagorean Theorem Proofs Quick Check

Question

3 of 5
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle. (1 point)
No, because 22 is not equal to 15 .
No, because 325 is not equal to 144 .
No, because 369 is not equal to 100 .
No, because 244 is not equal to 225 .

Answer 1

To determine whether a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first identify the longest side, which is 15. According to the theorem, for a triangle to be a right triangle, the square of the longest side (hypotenuse) should equal the sum of the squares of the other two sides.

Let's check if \( 15^2 = 10^2 + 12^2 \):

1. Calculate \( 15^2 \): \[ 15^2 = 225 \]

2. Calculate \( 10^2 \) and \( 12^2 \): \[ 10^2 = 100 \] \[ 12^2 = 144 \]

3. Now sum \( 10^2 + 12^2 \): \[ 100 + 144 = 244 \]

Now we compare:

• \( 15^2 = 225 \)
• \( 10^2 + 12^2 = 244 \)

Since \( 225 \) is not equal to \( 244 \), the triangle is not a right triangle.

Therefore, the correct explanation is: No, because 244 is not equal to 225.