A triangle has sides with lengths of 48 millimeters, 63 millimeters, and 80 millimeters. Is it a right triangle?
Question
A triangle has sides with lengths of 48 millimeters, 63 millimeters, and 80 millimeters. Is it a right triangle?
Solution
To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In this case, we can consider the longest side (80 mm) as the hypotenuse. So, we can plug the lengths of the sides into the equation:
48² + 63² = 80² 2304 + 3969 = 6400 6273 = 6400
Since 6273 is not equal to 6400, the triangle is not a right triangle.
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