Find angle and hypotenuse of right angled triangle

Question

Find the missing side and the hypotenuse of a right triangle that has a side length of 5 cm and a perimeter of 30 cm.

I'm confused. Can somebody please explain to me how to do this step by step? Not just the answer I want to know what you did to get the answer and why you did it please. Thank you!

Answer 1

Let $a,b$ be the two perpendicular sides of the triangle and $c$ be its hypotenuse. Then $a^2+b^2=c^2$. You have been given $a=5$ and $a+b+c=30$. This implies $b=25-c$. Can you do the rest?

Answer 2

Let one of other two sides is x then third side is 25-x.

By Pythagoras theorem, $x^2=5^2+(25-x)^2$

$x=13$, and it is the hypotenuse because it is the largest sides, third being 12.