To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) equals the square of the longest side (the hypotenuse).
First, we identify the longest side, which is 39. Therefore, we need to check if:
\[ 15^2 + 36^2 = 39^2 \]
Calculating each square:
- \( 15^2 = 225 \)
- \( 36^2 = 1296 \)
- \( 39^2 = 1521 \)
Now, adding the squares of the two shorter sides:
\[ 15^2 + 36^2 = 225 + 1296 = 1521 \]
Now we compare this result with the square of the longest side:
\[ 39^2 = 1521 \]
Since \( 15^2 + 36^2 = 39^2 \), the triangle is a right triangle.
The correct response is:
Yes, because 1,521 equals 1,521.