Question

A circular garden has a decorative, inscribed equilateral triangle pathway running through it. The total length of the pathway is 900 meters. The radius of the garden is \(k\sqrt{3}\) meters. What is the value of \(k\)?

Answer 1

Let the triangle side be s. Perimeter = 3s = 900, so s = 300.
For an equilateral triangle, the circumradius R = s/√3 = 300/√3 = 100√3.
Given R = k√3, we have k = 100.