## Challenge 248: A Triangle Challenge

In a particular right-angled triangle, the length of one of the sides is the average of the lengths of the other two sides.

Show that the area *A* and perimeter, *P*, of the triangle are related by *P ^{2 }= kA* for some number

*k,*and find the value of

*k*.

### Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide you with feedback on your solution.