If triangle ABC

Question

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.

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.

Yes, because 1,746 equals 1,746.
Yes, because 1,746 equals 1,746.
Remaining Attempts : 3

Answer 1

To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) equals the square of the longest side (the hypotenuse).

First, we identify the longest side, which is 39. Therefore, we need to check if:

\[ 15^2 + 36^2 = 39^2 \]

Calculating each square:

• \( 15^2 = 225 \)
• \( 36^2 = 1296 \)
• \( 39^2 = 1521 \)

Now, adding the squares of the two shorter sides:

\[ 15^2 + 36^2 = 225 + 1296 = 1521 \]

Now we compare this result with the square of the longest side:

\[ 39^2 = 1521 \]

Since \( 15^2 + 36^2 = 39^2 \), the triangle is a right triangle.

The correct response is:

Yes, because 1,521 equals 1,521.