What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 5 and 11?

Question

Abigail Armstrong · Accepted Answer

#sqrt146#

This is a job for the Pythagorean Theorem.

The Pythagorean Theorem takes the length of any two sides of a right triangle and tells you the length of the remaining side.

For a right triangle with leg lengths of #a# and #b# and a hypotenuse length of #c#, the Pythagorean Theorem states that

#a^2+b^2=c^2#

Here, we are given the two sides that are not the hypotenuse, which are #a# and #b#. We can substitute them into the equation to find the length of the hypotenuse, #c#.

#5^2+11^2=c^2#

Simplify.

#25+121=c^2#

#146=c^2#

#c=sqrt146#

This is as simplified as it can get, since the prime factorization of #146# is #2*73#.

Carter Anderson · Answer

undefined To find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known, we can use the Pythagorean theorem.

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.

Let's denote the lengths of the two sides as $a = 5$ and $b = 11$, and the length of the hypotenuse as $c$.

According to the Pythagorean theorem:

$$c^2 = a^2 + b^2$$

$$c^2 = 5^2 + 11^2$$

$$c^2 = 25 + 121$$

$$c^2 = 146$$

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

$$c = \sqrt{146}$$

Using a calculator, we find that $c \approx 12.083$.

So, the length of the hypotenuse of the right triangle is approximately 12.083 units.