Dealing with figures in LaTeX

Question

I have two figures I want them to be side-by-side, and I have two issues:

1) How to make both figures have the same size? I know that dimensions are not the same for both figures, but how can I make them the same? (both figures are in pdf format)

2) I want to include one caption for both figures.. say, Figure 1, but underneath the figure on the left side I want to put (a), and underneath the figure on right side I want to put (b).. so we have figure 1(a) and Figure 1(b).

This is ehat I have so far:

\begin{figure}
\centering
\mbox{\subfigure{\includegraphics[scale=0.5]{Figure1_a.pdf}
\quad
\subfigure{\includegraphics[scale=0.5]{Figure1_b.pdf} }}}
\caption{caption for figure 1}
\label{fig12}
\end{figure}

Answer 1

With graphicx you can set the width of the figure.

So you should do something like

\documentclass{article}
\usepackage{graphicx}
\pagestyle{empty}
\begin{document}

Same width

\includegraphics[width=2cm]{example-image-16x10}

\includegraphics[width=2cm]{example-image-10x16}
\vspace{1cm}

Same height

\begin{minipage}[t]{2in}
     \hspace*{\fill}\includegraphics[height=3cm]{example-image-16x10}\hspace*{\fill}\par
     \hspace*{\fill}Caption for first\hspace*{\fill}
\end{minipage}
\begin{minipage}[t]{2in}
    \hspace*{\fill}\includegraphics[height=3cm]{example-image-10x16}\hspace*{\fill}\par
     \hspace*{\fill}Caption for second\hspace*{\fill}
\end{minipage}
\vspace{1cm}

Same height and width (ick!)

\includegraphics[height=3cm,width=2cm]{example-image-16x10}
\includegraphics[height=3cm,width=2cm]{example-image-10x16}

\end{document}