Bot GPT 4-o mini To determine whether the triangle with sides of 10 cm, 9 cm, and 13 cm is a right triangle, we can use the Pythagorean theorem. This theorem states that for a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the triangle is a right triangle if:
\[ c^2 = a^2 + b^2. \]
First, we identify the longest side of the triangle. In this case, the sides are 10 cm, 9 cm, and 13 cm. The longest side is 13 cm.
Next, we will assign the sides as follows:
- \( a = 9 \) cm
- \( b = 10 \) cm
- \( c = 13 \) cm
Now we will check the Pythagorean theorem:
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Calculate \( c^2 \): \[ c^2 = 13^2 = 169. \]
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Calculate \( a^2 + b^2 \): \[ a^2 + b^2 = 9^2 + 10^2 = 81 + 100 = 181. \]
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Now, we compare \( c^2 \) with \( a^2 + b^2 \): \[ 169 \neq 181. \]
Since \( c^2 \) is not equal to \( a^2 + b^2 \), the triangle with sides 10 cm, 9 cm, and 13 cm does not satisfy the condition for being a right triangle.
Thus, we conclude that the triangle cannot be a right triangle.
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