Question

If a triangle has sides measuring 60 in., 75 in., and 45 in. in length, is it a right triangle? *Hint: Use the converse of the Pythagorean Theorem to check. Don't forget to use your Desmos calculator and STAAR Reference Sheet to help! (1 point) Responses No, because 9,225 does not equal 2,025. No, because 9,225 does not equal 2,025. Yes, because 3,600 equals 3,600. Yes, because 3,600 equals 3,600. No, because 5,625 does not equal 3,600. No, because 5,625 does not equal 3,600. Yes, because 5,625 equals 5,625.

Answer 1

To determine if the triangle with sides measuring 60 in, 75 in, and 45 in is a right triangle, we can utilize the converse of the Pythagorean Theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the longest side must equal the sum of the squares of the lengths of the other two sides.

1. Identify the longest side:
- The sides are 60 in, 75 in, and 45 in. The longest side is 75 in.

2. Apply the Pythagorean Theorem:
- \(a^2 + b^2 = c^2\)
- Where \(c\) is the longest side (75 in), and \(a\) and \(b\) are the other two sides (60 in and 45 in).

3. Calculate the squares:
- \(a^2 = 60^2 = 3600\)
- \(b^2 = 45^2 = 2025\)
- \(c^2 = 75^2 = 5625\)

4. Add \(a^2\) and \(b^2\):
- \(3600 + 2025 = 5625\)

5. Check if \(a^2 + b^2 = c^2\):
- \(5625 = 5625\)

Since \(a^2 + b^2 = c^2\) holds true, the triangle is a right triangle.

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