For the right triangle shown below, the lengths of two sides are given. Find the third side.

Leave your answer in simplified, radical form.

a = 5 b = 10 c = ?

The answer would be c = 11.2

5√5

Explanation:

The Pythagorean theorem is a^2 + b^2 = c^2. So in this case just plug in for known variables:

5^2 + 10^2 = c^2

Now solve for c:

25 + 100 = c^2

125 = c^2

√125 = √c^2

√125 = c

Now we must put our answer in simplified radical form. For this we have to think, what number can be divided out of 125, is a perfect square (has a square root as a whole number), and divides so that a whole number is left? How about 25?

125 / 25 = 5

now we have √25 · √5 = c

We know the square root of 25 so lets write this out in simplest form:

5√5 = c