Site S has a width of $20$ m. Write down the area of S.

Site T has the same area as site S, but a different width. Find the width of T.

When the width of the construction site is $b$ metres, the site has a maximum area.

(i)     Write down the value of $b$.

(ii)     Write down the maximum area.

The range of $A(x)$ is $m \leqslant A(x) \leqslant n$.

Hence write down the value of $m$ and of $n$.

$3600{\text{ (}}{{\text{m}}^2})$     (A1)(C1)

$x(200 - x) = 3600$     (M1)

Note: Award (M1) for setting up an equation, equating to their $3600$.

$180{\text{ (m)}}$     (A1)(ft)     (C2)

Note: Follow through from their answer to part (a).

(i)     $100{\text{ (m)}}$     (A1)     (C1)

(ii)     $10\,000{\text{ (}}{{\text{m}}^2})$     (A1)(ft)(C1)

Note: Follow through from their answer to part (c)(i).

$m = 3600\;\;\;$and$\;\;\;n = 10\,000$     (A1)(ft)     (C1)

Notes: Follow through from part (a) and part (c)(ii), but only if their $m$ is less than their $n$. Accept the answer $3600 \leqslant A \leqslant 10\,000$.