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lfdahl
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The shorter leg of an integer-sided right triangle has length 2001. How short
can the other leg be?
can the other leg be?
my solution:lfdahl said:The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?
An integer-sided right triangle is a triangle with three sides that are all whole numbers, and one of the angles is a right angle (90 degrees).
The leg lengths of the 2001 integer-sided right triangle are 2001 and 2672, as calculated by the Pythagorean theorem (a^2 + b^2 = c^2).
Yes, the minimum length for the other leg of an integer-sided right triangle is always 1. This is because the Pythagorean theorem states that the square of the hypotenuse (the longest side) must be equal to the sum of the squares of the other two sides. Therefore, the other leg cannot be less than 1, as it would result in a negative length.
Yes, an integer-sided right triangle can have equal leg lengths, as long as they are whole numbers and one of the angles is a right angle. This is known as an isosceles right triangle.
Yes, integer-sided right triangles have many practical applications in fields such as architecture, engineering, and surveying. They can be used to calculate distances, angles, and heights in real-world scenarios.