Question

If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point) Responses No, because 9,225 does not equal 2,025. No, because 9,225 does not equal 2,025. No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. Yes, because 3,600 equals 3,600. Yes, because 3,600 equals 3,600. Yes, because 5,625 equals 5,625.

Answer 1

To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can apply the Pythagorean theorem. For a triangle to be a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side.

Here are the side lengths:
- a = 45
- b = 60
- c = 75 (the longest side)

Now we check the Pythagorean theorem:

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

Calculating:

- \( 45^2 = 2025 \)
- \( 60^2 = 3600 \)
- \( 75^2 = 5625 \)

Now, add the squares of the shorter sides:

\[
2025 + 3600 = 5625
\]

Since \( 5625 = 5625 \), this means that

\[
45^2 + 60^2 = 75^2
\]

Therefore, the triangle is a right triangle.

The correct response is: **Yes, because 5,625 equals 5,625.**