What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
m^2+n^2=
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The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In algebraic form, it is represented as:
c^2 = a^2 + b^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In the given equation m^2 + n^2, it does not specify which side is the hypotenuse, but it represents the sum of the squares of the two other sides.
I apologize for the confusion. The equation m^2 + n^2 represents the sum of the squares of the lengths of the two sides of a right triangle, but it does not indicate the relationship between these sides. The Pythagorean Theorem, as mentioned earlier, states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using the Pythagorean Theorem formula, if m and n were the lengths of the legs of a right triangle, the length of the hypotenuse (let's say c) would be determined by:
c^2 = m^2 + n^2
In this case, the relationship is that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two sides. This relationship is always true in a right triangle, regardless of the values of m and n.
The Pythagorean Theorem 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.
In this case, the equation m^2 + n^2 = represents the Pythagorean Theorem, where m and n are the lengths of the two sides (legs) of the right triangle. The left side of the equation represents the sum of the squares of the two sides, while the right side represents the square of the length of the hypotenuse.
So, based on the Pythagorean Theorem, the relationship of the sides in this triangle is that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.