To determine if the triangle with sides measuring 60 in., 75 in., and 45 in. is a right triangle, we can use the converse of the Pythagorean Theorem. According to this theorem, a triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.
First, identify the longest side. In this case, the sides are:
- 60 in.
- 75 in. (longest side)
- 45 in.
Next, we can apply the Pythagorean Theorem:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the longest side, and \(a\) and \(b\) are the other two sides.
So we compute:
- \(c^2 = 75^2 = 5625\)
- \(a^2 = 60^2 = 3600\)
- \(b^2 = 45^2 = 2025\)
Now we add \(a^2\) and \(b^2\):
\[ 3600 + 2025 = 5625 \]
Now we compare \(c^2\) and \(a^2 + b^2\):
\[ 5625 = 5625 \]
Since these two values are equal, it confirms that the triangle is a right triangle.
Thus, the correct response is:
Yes, because 5,625 equals 5,625.
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