Question

A hotel 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.)

Answer 1

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.