To determine if a triangle with sides of lengths 60 meters, 79 meters, and 97 meters is a right triangle, we can apply the Pythagorean theorem. The Pythagorean theorem states that for a triangle to be a right triangle, the square of the length of the longest side (the hypotenuse) must equal the sum of the squares of the other two sides.
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Identify the longest side:
- The lengths of the sides are 60 m, 79 m, and 97 m. The longest side is 97 m.
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Apply the Pythagorean theorem:
- Check if \( a^2 + b^2 = c^2 \) where \( c \) is the longest side.
- Here, let \( a = 60 \) m, \( b = 79 \) m, and \( c = 97 \) m.
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Calculate:
- \( a^2 = 60^2 = 3600 \)
- \( b^2 = 79^2 = 6241 \)
- \( c^2 = 97^2 = 9409 \)
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Now check if \( a^2 + b^2 = c^2 \):
- \( 3600 + 6241 = 9841 \)
- \( 9409 \neq 9841 \)
Since \( a^2 + b^2 \) does not equal \( c^2 \), the triangle with sides of lengths 60 meters, 79 meters, and 97 meters is not a right triangle.