2024 CGSS P1 Q1

Two cylinders are such that the ratio of their heights is \(\sqrt{7} : 1\).
The height of the smaller cylinder is \(\frac{2\sqrt{7} - 1}{(2 - \sqrt{7})^2}\) cm.
Without using a calculator, find the height of the larger cylinder, expressing your answer in the form \((a + b\sqrt{7})\) cm, where \(a\) and \(b\) are integers.[4]