Area SM-Bank 049

A rectangle has an area of 24 square centimetres.

One possible pair of integer dimensions for this rectangle is \(2\ \text{cm}\times 12\ \text{cm}\).
Write down all possible pairs of integer dimensions for a rectangle with an area of 24 square centimetres. (2 marks)

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Using the given dimensions and your answers from (a), calculate the largest possible perimeter for a rectangle with an area of 24 square centimetres. (2 marks)

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a. \(1\ \text{cm}\times 24\ \text{cm}, 2\ \text{cm}\times 12\ \text{cm}, 3\ \text{cm}\times 8\ \text{cm}, 4\ \text{cm}\times 6\ \text{cm}\)

b. \(50\ \text{cm}\)

Show Worked Solution

a. \(\text{All possible integer dimensions:}\)

\(1\ \text{cm}\times 24\ \text{cm},\ \ 2\ \text{cm}\times 12\ \text{cm},\ \ 3\ \text{cm}\times 8\ \text{cm},\ \ 4\ \text{cm}\times 6\ \text{cm}\)

b. \(\text{Perimeters}\)

\(\text{P}_{1}=2\times 1+2\times 24=50\ \text{cm}\)

\(\text{P}_{2}=2\times 2+2\times 12=28\ \text{cm}\)

\(\text{P}_{3}=2\times 3+2\times 8=22\ \text{cm}\)

\(\text{P}_{4}=2\times 4+2\times 6=20\ \text{cm}\)

\(\therefore\ \text{Largest possible perimeter}= 50\ \text{cm}\)