Question

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.

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, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Here, the sides are:
- a = 15
- b = 36
- c = 39 (the longest side, which we assume to be the hypotenuse)

Now we check:

1. Calculate the squares of the lengths of the two shorter sides (a and b):
- \( a^2 = 15^2 = 225 \)
- \( b^2 = 36^2 = 1296 \)

2. Add these squares together:
- \( a^2 + b^2 = 225 + 1296 = 1521 \)

3. Calculate the square of the length of the hypotenuse (c):
- \( c^2 = 39^2 = 1521 \)

Now we compare \( a^2 + b^2 \) to \( c^2 \):

- \( a^2 + b^2 = 1521 \)
- \( c^2 = 1521 \)

Since \( 1521 = 1521 \), the triangle satisfies the Pythagorean theorem.

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