Question

If a triangle has sides measuring 60, 75, and 45, is it a right triangle? Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.

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

No, because 9,225 does not equal 2,025.
No, because 9,225 does not equal 2,025.

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

Answer 1

To determine whether the triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. For a triangle to be a right triangle, the following must hold true:

\( c^2 = a^2 + b^2 \)

where \( c \) is the length of the longest side (the hypotenuse) and \( a \) and \( b \) are the lengths of the other two sides.

In this case, the lengths are:

- \( a = 45 \)
- \( b = 60 \)
- \( c = 75 \) (the longest side)

Now we calculate:

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

2. Calculate \( a^2 + b^2 \):
\[
a^2 + b^2 = 45^2 + 60^2 = 2025 + 3600 = 5625
\]

Now we compare \( c^2 \) and \( a^2 + b^2 \):
\[
5625 = 5625
\]

Since they are equal, the triangle with sides measuring 60, 75, and 45 **is** a right triangle.

Thus, the correct statement is:
**Yes, because 5,625 equals 5,625.**