Which of the following numbers completes the Pythagorean triple: 12, 16,
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.
So, in this case, we have a right triangle with sides of length 12 and 16.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
Therefore, c = √400 = 20.
So, the number 20 completes the Pythagorean triple: 12, 16, 20.
To determine which number completes the Pythagorean triple, we need to apply the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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.
So, for the triple 12, 16, x, we need to find the value of x.
Let's apply the Pythagorean theorem:
According to the theorem, we have:
12^2 + 16^2 = x^2
Simplifying this equation, we get:
144 + 256 = x^2
400 = x^2
To find the value of x, we need to find the square root of 400, which is:
x = sqrt(400)
Calculating the square root of 400, we find:
x = 20
Therefore, the missing number that completes the Pythagorean triple is 20.
To find the missing number in the Pythagorean triple, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides we have are 12 and 16. Let's assume the missing number is x.
According to the Pythagorean theorem, we have:
12^2 + 16^2 = x^2
Simplifying this equation, we get:
144 + 256 = x^2
400 = x^2
To determine the value of x, we can take the square root of both sides:
√400 = √x^2
20 = x
Therefore, the missing number in the Pythagorean triple is 20.