2006-I-11 – Solving Master

Ans: (a)

0.5 cm

(b)

223 {cm}^{2}

(c)

223 \leq x < 270

The maximum absolute error
$\begin{array}{cl} = & 1 \div 2 \\ = & 0.5 cm \end{array}$
Add a point $G$ on $A F$ such that $A F ⊥ D G$ and $C D G$ is a straight line.

The least possible total area

$\begin{array}{cl} = & the least possible area of A B C G + the least possible area of D E F G \\ = & 17.5 \times 11.5 + 1.5 \times 14.5 \\ = & 223 {cm}^{2} \end{array}$
The greatest possible total area
$\begin{array}{cl} = & the greatest possible area of A B C G + the greatest possible area of D E F G \\ = & 18.5 \times 12.5 + 2.5 \times 15.5 \\ = & 270 {cm}^{2} \end{array}$

Hence, we have $223 \leq x < 270$ .