What is the length of the third side of a right triangle if it is known that the two of the sides have lengths 5 and 13. How many solutions does this problem have?

Step-by-step explanation:

We are given with the two sides of a right angled triangle having lengths of 5 and 13. It is required to find the length of the third side of a right triangle. We know that hypotenuse of right angled triangle is the longest side.

For right angle triangle, we use Pythagoras theorem as:

H²=P²+B²

P is perpendicular distance

B is base

Putting H = 13 and P = 5, then

B² = H²-P²

B² = (13) ² - (5) ²

B²=144

B=12

So, the length if the third side of a right triangle is 12. It is the only solution.