If triangle ABC

Question

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

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.
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

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 for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), the following equation holds:

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

First, we will identify the lengths of the sides. The longest side (which would be the hypotenuse if this were a right triangle) is 39. Thus, we have:

• \( a = 15 \)
• \( b = 36 \)
• \( c = 39 \)

Next, we calculate \( a^2 + b^2 \) and \( c^2 \):

1. \( a^2 + b^2 = 15^2 + 36^2 = 225 + 1296 = 1521 \)
2. \( c^2 = 39^2 = 1521 \)

Since \( a^2 + b^2 = c^2 \) (1521 = 1521), triangle ABC is a right triangle.

Thus, the correct response is:

Yes, because 1,521 equals 1,521.