Question

If a triangle has sides measuring 60 in., 75 in., and 45 in. in length, 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.

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.
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 apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

1. Identify the lengths of the sides:
- \( a = 45 \, \text{in} \)
- \( b = 60 \, \text{in} \)
- \( c = 75 \, \text{in} \) (hypotenuse, since it is the longest side)

2. Apply the Pythagorean theorem:
- Calculate \( a^2 + b^2 \):
\[
45^2 + 60^2 = 2025 + 3600 = 5625
\]

- Calculate \( c^2 \):
\[
75^2 = 5625
\]

3. Compare the two results:
- Since \( a^2 + b^2 = c^2 \) (i.e., \( 5625 = 5625 \)), the triangle satisfies the Pythagorean theorem.

Therefore, the triangle with sides measuring 60 in., 75 in., and 45 in. **is a right triangle**.

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