Edexcel C1 — Question 3

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicIndices and Surds

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c4ae1bec-12f4-492d-8027-bba4840ff545-2_337_1235_781_383} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the rectangles \(A B C D\) and \(E F G H\) which are similar.
Given that \(A B = ( 3 - \sqrt { 5 } ) \mathrm { cm } , A D = \sqrt { 5 } \mathrm {~cm}\) and \(E F = ( 1 + \sqrt { 5 } ) \mathrm { cm }\), find the length \(E H\) in cm, giving your answer in the form \(a + b \sqrt { 5 }\) where \(a\) and \(b\) are integers.