The diagram shows a rectangular garden of length \(12\) m and width \(7.5\) m. The length is increased by \(20\%\) and the width is decreased by \(10\%\). C...
Question 1 Report
The diagram shows a rectangular garden of length \(12\) m and width \(7.5\) m.
The length is increased by \(20\%\) and the width is decreased by \(10\%\).
Calculate the area of the new rectangle.
Answer Details
Each side changes by its own percentage, so adjust the length and the width separately and only then multiply to find the new area. Area is not found by changing the original area by \(20\%\) and \(10\%\) in one step.
- New length: an increase of \(20\%\) gives a multiplier of \(1.2\). \[ 12\times 1.2 = 14.4 \text{ m} \] [M1]
- New width: a decrease of \(10\%\) gives a multiplier of \(0.9\). \[ 7.5\times 0.9 = 6.75 \text{ m} \] [M1]
- New area: \[ 14.4\times 6.75 = 97.2 \text{ m}^2 \]
The area of the new rectangle is \(97.2\) m\(^2\) [A1]
Notice that the percentage changes do not cancel out. The original area was \(12\times 7.5 = 90\) m\(^2\), and the combined multiplier is \(1.2\times 0.9 = 1.08\), an \(8\%\) increase, giving \(90\times 1.08 = 97.2\) m\(^2\) as a check. Assuming a \(20\%\) rise and a \(10\%\) fall leave a net \(10\%\) rise on the area is the standard misconception here.
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