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 39 squared plus 15 squared not equal to 36 squared
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.
Responses
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.
Yes, because 1,521 equals 1,521.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
Answers
GPT-4o mini
To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can use the Pythagorean theorem, which states that if a triangle is a right triangle, then the square of the length of the hypotenuse (the longest side) must equal the sum of the squares of the lengths of the other two sides.
Here, the sides are:
- a = 15
- b = 36
- c = 39 (hypotenuse)
Now, let's apply the theorem:
1. Calculate \(15^2 + 36^2\):
\[
15^2 = 225
\]
\[
36^2 = 1296
\]
\[
15^2 + 36^2 = 225 + 1296 = 1521
\]
2. Calculate \(39^2\):
\[
39^2 = 1521
\]
Since \(15^2 + 36^2 = 39^2\) (i.e., \(1521 = 1521\)), the triangle satisfies the Pythagorean theorem.
Therefore, the correct response is:
**Yes, because 1,521 equals 1,521.**
Here, the sides are:
- a = 15
- b = 36
- c = 39 (hypotenuse)
Now, let's apply the theorem:
1. Calculate \(15^2 + 36^2\):
\[
15^2 = 225
\]
\[
36^2 = 1296
\]
\[
15^2 + 36^2 = 225 + 1296 = 1521
\]
2. Calculate \(39^2\):
\[
39^2 = 1521
\]
Since \(15^2 + 36^2 = 39^2\) (i.e., \(1521 = 1521\)), the triangle satisfies the Pythagorean theorem.
Therefore, the correct response is:
**Yes, because 1,521 equals 1,521.**