To determine if the triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. The theorem states that for a right triangle with sides \( a \), \( b \), and hypotenuse \( c \) (where \( c \) is the longest side), the following equation must hold:
\[ c^2 = a^2 + b^2 \]
Given that the sides are 60, 75, and 45, we identify the longest side \( c \) as 75. Therefore, we check if:
\[ 75^2 = 60^2 + 45^2 \]
Calculating each term:
- \( 75^2 = 5625 \)
- \( 60^2 = 3600 \)
- \( 45^2 = 2025 \)
Now, we add \( 60^2 \) and \( 45^2 \):
\[ 3600 + 2025 = 5625 \]
Since both sides match (\( 5625 = 5625 \)), we conclude that the triangle is a right triangle.
The correct response is:
Yes, because 5,625 equals 5,625.