Question

Pythagorean Theorem Proofs Quick Check 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 325 is not
equal to 144.
No, because 244 is not
equal to 225.
No, because 369 is not
equal to 100.
No, because 22 is not
equal to 15

Answer 1

To determine if the triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the longest side. In this case, the longest side is 15.

According to the Converse of the Pythagorean Theorem, a triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.

Let's check this:

1. Longest side (c) = 15
2. Other sides (a and b) = 10 and 12

We need to check if:

\[ c^2 = a^2 + b^2 \]

Calculating the squares:

- \( c^2 = 15^2 = 225 \)
- \( a^2 = 10^2 = 100 \)
- \( b^2 = 12^2 = 144 \)

Now, sum the squares of the other two sides:

\[ a^2 + b^2 = 100 + 144 = 244 \]

Now we can compare:

\[ c^2 (225) \neq a^2 + b^2 (244) \]

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

The correct choice from the options provided is:

**No, because 244 is not equal to 225.**