triangle ABC

Question

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.

Yes, because 1,521 equals 1,521.
Yes, because 1,521 equals 1,521.

No, because 392+152≠362
No, because 39 squared plus 15 squared not equal to 36 squared

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.
Remaining Attempts : 3

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 (the hypotenuse) must equal the sum of the squares of the other two sides.

1. Identify the longest side: In this case, the longest side is 39.
2. Apply the Pythagorean theorem:
   • \(a^2 + b^2 = c^2\), where \(c\) is the longest side (39).

Calculating the squares of the sides:

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

Now check if the sum of the squares of the other two sides equals the square of the longest side: \[ 15^2 + 36^2 = 225 + 1296 = 1521 \] Since \(1521 = 39^2\), the condition of the Pythagorean theorem is satisfied.

Thus, the answer is: Yes, because 1,521 equals 1,521.