4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{4d5b914c-28b2-4485-a42e-627c95fa16e2-16_581_961_251_552}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

Figure 2 shows a sketch of the parabola with equation $y = \frac { 1 } { 2 } x ( 10 - x ) , 0 \leqslant x \leqslant 10$ This question concerns rectangles that lie under the parabola in the first quadrant.The bottom edge of each rectangle lies along the $x$-axis and the top left vertex lies on the parabola.Some examples are shown in Figure 2.

Let the $x$ coordinate of the top left vertex be $a$ .
\begin{enumerate}[label=(\alph*)]
\item Explain why the width,$w$ ,of such a rectangle must satisfy $w \leqslant 10 - 2 a$
\item Find the value of $a$ that gives the maximum area for such a rectangle.

Given that the rectangle must be a square,
\item find the value of $a$ that gives the maximum area for such a square.

Given that the area of the rectangles is fixed as 36
\item find the range of possible values for $a$ .\\
\includegraphics[max width=\textwidth, alt={}, center]{4d5b914c-28b2-4485-a42e-627c95fa16e2-16_2255_50_311_1980}
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2020 Q4 [17]}}