Question

If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)
Responses

Yes, because 5,625 equals 5,625.
Yes, because 5,625 equals 5,625.

No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.

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.

Answer 1

To determine if the triangle with sides measuring 60, 75, and 45 is a right triangle, we can apply the Pythagorean theorem, which 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 sides: Here, the sides are 60, 75, and 45. The longest side is 75.

2. Calculate the squares of the sides:
- \( 75^2 = 5625 \)
- \( 60^2 = 3600 \)
- \( 45^2 = 2025 \)

3. Check the Pythagorean theorem:
\( 75^2 \stackrel{?}{=} 60^2 + 45^2 \)
\( 5625 \stackrel{?}{=} 3600 + 2025 \)
\( 5625 \stackrel{?}{=} 5625 \)

Since both sides of the equation are equal, we can conclude that:

**Yes, because 5,625 equals 5,625.**