The diagram shows a rectangular field measuring \(62\) m by \(48\) m. Each measurement is correct to the nearest metre. (a) Calculate the upper bound of the...

Each measurement is correct to the nearest metre, so the half-unit is \(0.5\) m. The length lies between \(61.5\) m and \(62.5\) m, and the width between \(47.5\) m and \(48.5\) m. Every part below picks the bounds that push the required quantity in the stated direction.

(a) Area is a product, so the greatest area uses both upper bounds:

\(62.5 \times 48.5\) [M1]

\(= 3031.25\) m\(^2\) [A1]

(b) Perimeter is a sum, so the least perimeter uses both lower bounds:

\(2 \times (61.5 + 47.5)\) [M1]

\(= 2 \times 109 = 218\) m [A1]

(c) The cost is the perimeter multiplied by a fixed price per metre, and since the price is exact the cost is greatest when the perimeter is greatest. That means both upper bounds again:

\(2 \times (62.5 + 48.5) \times 4.75\) [M1]

\(= 222 \times 4.75 = 1054.5\), so the upper bound of the cost is \(\$1054.50\). [A1]

Money answers are written to 2 decimal places, so \(\$1054.50\) rather than \(\$1054.5\). Note that part (c) does not reuse the answer to part (b): part (b) asked for the lower bound of the perimeter, whereas the greatest cost needs the upper bound.