If triangle ABC has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point) Responses Yes, because 1,746 equals 1,746. Yes, because 1,746 equals 1,746. No, because 392+152 ≠362 No, because 392+152 ≠362 Yes, because 1, 521 equals 1,521. Yes, because 1, 521 equals 1,521. No, because the sum of the squared legs do not equal the square root of the hypotenuse.

1 answer

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.