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

Question

No, because 9,225 does not equal
2,025.
• Yes, because 5,625 equals 5,625.
No, because 5,625 does not equal
3,600.
• Yes, because 3,600 equals 3,600.

Answer 1

To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. The 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.

Identifying the longest side:

• The sides are 60, 75, and 45.
• The longest side is 75.

Now we can apply the Pythagorean theorem:

1. Calculate the squares of the sides:

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

2. Verify the Pythagorean theorem:

   • We need to check if \( 75^2 = 60^2 + 45^2 \)
   • This means we need to see if \( 5625 = 3600 + 2025 \)

3. Calculate the right-hand side:

   • \( 3600 + 2025 = 5625 \)

Since both sides are equal:

• \( 5625 = 5625 \)

Therefore, the answer is Yes, because 5,625 equals 5,625.