If a triangle has sides of length 12 and 16, how long is the hypotenuse?(1 point)
To determine the length of the hypotenuse, 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.
Let's denote the sides of the triangle as follows:
- The length of the first side (adjacent to the right angle) is a = 12.
- The length of the second side (opposite to the right angle) is b = 16.
- The length of the hypotenuse is c.
The Pythagorean theorem is expressed as:
c² = a² + b²
Substituting the given values, we have:
c² = 12² + 16²
c² = 144 + 256
c² = 400
Taking the square root of both sides, we find:
c = √400
c = 20
Therefore, the length of the hypotenuse of the triangle is 20.
To find the length of the hypotenuse of a triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
So, we have a triangle with sides of length 12 and 16.
Let's label the sides:
a = 12
b = 16
c = hypotenuse (which we want to find)
Using the Pythagorean theorem, we can write the equation as:
c^2 = a^2 + b^2
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
To find the length of the hypotenuse (c), we need to take the square root of both sides of the equation:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
To find the length of the hypotenuse of a triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the two given sides are 12 and 16. Let's assume that the side of length 12 is one of the legs of the right triangle, and the side of length 16 is the other leg.
So, applying the Pythagorean theorem, we can write:
c² = a² + b²
c² = 12² + 16²
c² = 144 + 256
c² = 400
To solve for c, we need to take the square root of both sides:
c = √400
Taking the square root of 400 gives us:
c = 20
Therefore, the length of the hypotenuse is 20.