Question

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.

Answer 1

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.**