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. This 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.
First, we identify the longest side, which is 75 in. So let’s use this as the hypotenuse (c), and the other two sides (a = 60 in. and b = 45 in.):
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Calculate \( c^2 \):
\( 75^2 = 5625 \) -
Calculate \( a^2 + b^2 \):
\( 60^2 + 45^2 = 3600 + 2025 = 5625 \)
Now we compare the two results:
- \( c^2 = 5625 \)
- \( a^2 + b^2 = 5625 \)
Since \( c^2 \) equals \( a^2 + b^2 \) (both equal 5625), the triangle with sides 60 in., 75 in., and 45 in. is indeed a right triangle.
Therefore, the correct answer is: Yes, because 5,625 equals 5,625.