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 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.

No, because 392+152≠362

Answer 1

To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem. For a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) must equal the sum of the squares of the lengths of the other two sides.

1. Identify the longest side:
- The sides are 39, 15, and 36. The longest side is 39.

2. Apply the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the hypotenuse (39) and \( a \) and \( b \) are the other two sides (15 and 36).

3. Calculate the squares:
\[
39^2 = 1521
\]
\[
15^2 = 225
\]
\[
36^2 = 1296
\]

4. Add the squares of the two shorter sides:
\[
15^2 + 36^2 = 225 + 1296 = 1521
\]

Now we can compare:
\[
39^2 (1521) = 15^2 + 36^2 (1521)
\]

Since both sides are equal (1521 = 1521), triangle ABC is a right triangle.

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