To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem. In a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.
Let's identify the sides:
- 39 (the longest side)
- 36
- 15
Now, we apply the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse (39 in this case), and \(a\) and \(b\) are the lengths of the other two sides:
\[ 39^2 = 36^2 + 15^2 \]
Calculating the squares:
\[ 39^2 = 1521 \] \[ 36^2 = 1296 \] \[ 15^2 = 225 \]
Now, add \(36^2\) and \(15^2\):
\[ 36^2 + 15^2 = 1296 + 225 = 1521 \]
Since \(39^2 = 1521\) and \(36^2 + 15^2 = 1521\), we see that:
\[ 39^2 = 36^2 + 15^2 \]
Therefore, triangle ABC is indeed a right triangle.
The correct response is: Yes, because 1,521 equals 1,521.
1 answer