Ahotel wants to put a fence around a circular spa. the radius of the spa is 5/√2-1 feet. if the fence is built along the immediate edge of the spa, what is the perimeter of the fence? (recall that the
perimeter of a circle is 2πr , where r is the radius of the circle.)

It is important to look at all the information's that are given in the question very closely. Let us write them write first.

Radius of the spa = 5/√2-1 feet
Now
Perimeter of the circle = 2πr
                                    = 2π (5/√2-1) 
                                    = π(5/(√2-1)*(√2+1)/(√2+1) 
                                    = 2π(5/(√2+1))/(2-1) 
                                    = 10π(√2+1)  

I hope that the procedure is clear enough for you to understand.