What is the length of the hypotenuse of a right triangle with legs of 5 and 12 units?

What is the "hypotenuse" and "legs" of a triangle? Thanks!

The two legs form the right angle and the hypotenuse is the longest side, being opposite the right angle.

In any right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse.

x^2 + y^2 = z^2

You have the two sides of 5 and 12 from which, the hypotenuse is equal to the square root of (5^2 + 12^2) = 13.

In a right triangle, the hypotenuse is the side opposite the right angle and is the longest side of the triangle. The legs are the two shorter sides that meet at the right angle.

To find the length of the hypotenuse, we can use the Pythagorean theorem. The 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 two legs.

So, to find the length of the hypotenuse, we can use the equation:

c^2 = a^2 + b^2

where c represents the length of the hypotenuse, and a and b represent the lengths of the legs.

In this case, the given lengths of the legs are 5 and 12 units, so substituting those values into the equation, we have:

c^2 = 5^2 + 12^2

Simplifying this equation, we get:

c^2 = 25 + 144
c^2 = 169

To find the length of the hypotenuse, we take the square root of both sides:

c = √169
c = 13

Therefore, the length of the hypotenuse of the right triangle with legs of 5 and 12 units is 13 units.