Question

If triangle ABC
has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
Responses

No, because 392+152 ≠362

No, because 392+152 ≠362
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
Yes, because 1, 521 equals 1,521.
Yes, because 1, 521 equals 1,521.
Yes, because 1,746 equals 1,746.

Answer 1

To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can apply the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) equals the sum of the squares of the lengths of the other two sides.

1. Identify the lengths of the sides: 39, 15, and 36. The longest side (hypotenuse) is 39.
2. Check the Pythagorean theorem:

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

where:
- \( a = 15 \)
- \( b = 36 \)
- \( c = 39 \)

3. Calculate:

\[
15^2 + 36^2 = 225 + 1296 = 1521
\]

\[
39^2 = 1521
\]

Since \( 15^2 + 36^2 = 39^2 \), this means that the triangle is a right triangle.

Therefore, the correct response is:

**Yes, because 1,521 equals 1,521.**