Question

The side lengths of a triangle are 4 inches, 6 inches, and 9 inches. Is this triangle a right

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a right triangle because the square of the longest side is
the sum of the squares of the shorter sides.

Answer 1

After applying the Pythagorean theorem, it's clear that a triangle with sides of 4, 6, and 9 inches is not a right triangle because the sum of the squares of the two shorter sides does not equal the square of the longest side.

Step-by-step explanation:

To determine whether a triangle with side lengths of 4 inches, 6 inches, and 9 inches is a right triangle, we can use the Pythagorean theorem.

According to the theorem, 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.

To check this, we calculate: 4² + 6²

= 16 + 36

= 52 and 9² = 81.

Because 52 is not equal to 81, the triangle with sides of lengths 4, 6, and 9 inches is not a right triangle.