To determine whether the triangle with side lengths 4, 8, and 9 is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) equals the sum of the squares of the lengths of the other two sides.
Let's identify the sides:
- Side 1: 4
- Side 2: 8
- Side 3 (hypotenuse): 9 (since it is the longest side)
Now, let's apply the Pythagorean theorem:
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Calculate \( 4^2 + 8^2 \): \[ 4^2 = 16 \] \[ 8^2 = 64 \] \[ 4^2 + 8^2 = 16 + 64 = 80 \]
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Calculate \( 9^2 \): \[ 9^2 = 81 \]
Now we compare:
- \( 4^2 + 8^2 = 80 \)
- \( 9^2 = 81 \)
Since \( 80 ≠ 81 \), this means the triangle is not a right triangle.
Thus, the correct answer is: B. No, because \( 4^2 + 8^2 ≠ 9^2 \).