Change \textheight in function of width

Question

Good day. I want define an environment that change the text height in function of the width

\documentclass[a4paper]{book}
\usepackage{lipsum}

\begin{document}
\the\textwidth---\the\textheight

\newenvironment{whtext}[1]{%
\newpage\begingroup
\hsize=#1 
\vsize=\dimexpr\textheight*\numexpr\hsize/\textwidth\relax  
\textwidth=\hsize
\textheight=\vsize}%
{\endgroup\newpage}


\lipsum[1-10]

\begin{whtext}{15cm}
\the\textwidth---\the\textheight
\lipsum[1-20]
\the\textwidth---\the\textheight
\end{whtext}

\end{document}

what i should do?

Answer 1

It's not a good idea to manipulate textheight etc. directly. The geometry package provides the means for doing this with \newgeometry, however, the price is a \clearpage\newpage

\documentclass[a4paper]{book}
\usepackage{geometry}
\usepackage{lipsum}

\begin{document}
\the\textwidth---\the\textheight

\newenvironment{whtext}[1]{%
\newpage\begingroup
\hsize=#1 
\vsize=\dimexpr\textheight*\numexpr\hsize/\textwidth\relax  
\newgeometry{textheight=\vsize,textwidth=\hsize}
 }%
{\endgroup\newpage}


\lipsum[1-10]

\begin{whtext}{15cm}
\the\textwidth---\the\textheight

\lipsum[1-20]
\the\textwidth---\the\textheight
\end{whtext}

\begin{whtext}{10cm}
\the\textwidth---\the\textheight

\lipsum[1-20]
\the\textwidth---\the\textheight
\end{whtext}

\end{document}

Answer 2

I think I have an answer

\documentclass[a4paper]{book}
\usepackage{lipsum}

\begin{document}
\the\textwidth---\the\textheight

\makeatletter
\newenvironment{whtext}[1]{%
\newpage\begingroup
\hsize=#1 
\vsize=\dimexpr\textheight*\hsize/\textwidth\relax  
\textwidth=\hsize
\textheight=\vsize}%
{\endgroup\newpage}
\makeatother

\lipsum[1-10]

\begin{whtext}{15cm}
\the\textwidth---\the\textheight
\lipsum[1-20]
\the\textwidth---\the\textheight
\end{whtext}

\end{document}