Check whether the triangle with the side lengths 5 cm, 7 cm, and 9 cm is an acute, right, or obtuse triangle.

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Solution

The longest side of the triangle has a length of $9 c m$ . Compare the square of the length of the longest side and the sum of squares of the other two sides.
Square of the length of the longest side is $9^{2} = 81$
Sum of the squares of the other two sides is
$5^{2} + 7^{2} = 25 + 49 = 74$
That is $81 > 74, 9^{2} > 5^{2} + 7^{2}$ .
Therefore, by the corollary to the converse of the Pythagorean Theorem, the triangle is an obtuse triangle.

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Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is

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