Standard +0.3 This is a straightforward similar rectangles problem requiring ratio setup and surds manipulation. Students must equate ratios AB/AD = EF/EH, substitute given values, and rationalize to reach the required form. While it involves surds, the steps are mechanical and typical for C1 level, making it slightly easier than average.
3.
\includegraphics[max width=\textwidth, alt={}, center]{4fec0924-d727-4d4f-81e6-918e1ccfedbd-1_330_1230_829_386}
The diagram 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.
3.\\
\includegraphics[max width=\textwidth, alt={}, center]{4fec0924-d727-4d4f-81e6-918e1ccfedbd-1_330_1230_829_386}
The diagram 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.\\
\hfill \mbox{\textit{OCR C1 Q3 [5]}}