Forcing subfigures to have same height and take overall X% of linewidth in LaTeX

You can include them to the same (more or less arbitrary) height then scale them together to the desired width

\documentclass{article}

\usepackage{graphicx}% images from mwe package

\begin{document}

\noindent X\dotfill X

\begin{center}
\resizebox{.9\textwidth}{!}{%
\includegraphics[height=3cm]{example-image-a}%
\quad
\includegraphics[height=3cm]{example-image-16x9}%
}
\end{center}

\end{document}

You can use the subcaption package and do the computation as suggested by David.

\documentclass{article}

\usepackage{graphicx}% images from mwe package
\usepackage{subcaption}

\newlength{\twosubht}
\newsavebox{\twosubbox}

\begin{document}

\noindent\hrulefill The text width\hrulefill

\begin{center}
\makebox[.9\textwidth]{\hrulefill 90\% of text width\hrulefill}
\end{center}

\begin{figure}[htp]

% preliminary
\sbox\twosubbox{%
  \resizebox{\dimexpr.9\textwidth-1em}{!}{%
    \includegraphics[height=3cm]{example-image-a}%
    \includegraphics[height=3cm]{example-image-16x9}%
  }%
}
\setlength{\twosubht}{\ht\twosubbox}

% typeset

\centering

\subcaptionbox{First\label{f}}{%
  \includegraphics[height=\twosubht]{example-image-a}%
}\quad
\subcaptionbox{Second\label{s}}{%
  \includegraphics[height=\twosubht]{example-image-16x9}%
}

\caption{The caption}

\end{figure}

\end{document}