A triangle has sides with lengths of 7 kilometers, 12 kilometers, and 13 kilometers. Is it a right triangle?
Question
A triangle has sides with lengths of 7 kilometers, 12 kilometers, and 13 kilometers. Is it a right triangle?
Solution
Yes, it is a right triangle. This is because it follows 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, if we consider 7 km and 12 km as sides a and b, and 13 km as the hypotenuse c, we can substitute these values into the theorem:
7² + 12² = 13² 49 + 144 = 169 193 = 169
Since both sides of the equation are equal, the triangle with sides 7 km, 12 km, and 13 km is a right triangle.
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