Question

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

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 1,746 equals 1,746.
Yes, because 1,746 equals 1,746.

No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared

Yes, because 1,521 equals 1,521.

Answer 1

To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem. A triangle is a right triangle if 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 sides:
- a = 15
- b = 36
- c = 39 (the longest side, potentially the hypotenuse)

2. Apply the Pythagorean theorem:
- Check if \( a^2 + b^2 = c^2 \):
\[
15^2 + 36^2 = 39^2
\]
\[
225 + 1296 = 1521
\]
\[
1521 = 1521
\]

Since the equation holds true, triangle ABC is indeed a right triangle.

The correct response is:
**Yes, because 1,521 equals 1,521.**