What is the relationship of the sides in this triangle based on the Pythagorean theorem? If n is 62 and m is 28, m to the second power + n to the second power equals what?
According to the Pythagorean theorem, the relationship of the sides in a right triangle can be expressed as follows:
a^2 + b^2 = c^2
Here, a and b represent the lengths of the two legs of the right triangle, while c represents the length of the hypotenuse.
In your question, the values given are n = 62 and m = 28.
Using the Pythagorean theorem, we can find the value of c^2:
m^2 + n^2 = c^2
(28)^2 + (62)^2 = c^2
784 + 3844 = c^2
4628 = c^2
So, m^2 + n^2 equals 4628.
To understand the relationship between the sides of a triangle based on the Pythagorean theorem, let's go through the steps:
1. 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.
2. In a triangle with sides labeled a, b, and c, where c is the hypotenuse, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
3. In this case, you provided two side lengths: n = 62 and m = 28. Let's substitute these values into the equation:
m^2 + n^2 = c^2
(28)^2 + (62)^2 = c^2
784 + 3844 = c^2
4628 = c^2
Therefore, the sum of the squares of the lengths of the sides (28 and 62) is equal to 4628.
To determine the relationship of the sides in a triangle based on the Pythagorean theorem, we first need to understand the theorem itself. The Pythagorean theorem states that in a right-angled 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 your example, you have given the values of two sides, n and m, and want to find the square of the length of the hypotenuse. The hypotenuse is usually represented by the variable c.
To apply the Pythagorean theorem, we can substitute the given values into the equation:
c² = m² + n²
Given:
m = 28
n = 62
Substituting these values into the equation:
c² = 28² + 62²
To find the answer, we need to evaluate the expression on the right-hand side of the equation:
c² = 784 + 3844
c² = 4628
Therefore, the equation m² + n² equals 4628.