Two rectangular advertising posters at a bus stop are mathematically similar in shape. The smaller poster has a width of 40 cm and an area of 1200 cm². The ...
Question 1 Report
Two rectangular advertising posters at a bus stop are mathematically similar in shape. The smaller poster has a width of 40 cm and an area of 1200 cm². The larger poster has a width of 60 cm. The transport company is checking that print costs scale correctly between the two sizes.
Work out the area of the larger poster. (4)
Answer Details
The two posters are mathematically similar rectangles, so their areas scale by the square of the linear scale factor between their matching widths.
\[ \text{Scale factor} = \frac{60}{40} = 1.5 \]\[ \text{Area scale factor} = 1.5^2 = 2.25 \]\[ \text{Larger area} = 1200 \times 2.25 = 2700 \text{ cm}^2 \]The area of the larger poster is \(2700\) cm\(^2\). [4] (1 for the scale factor 1.5, 1 for squaring it to 2.25, 1 for \(1200 \times 2.25\), 1 for 2700 cm\(^2\))
Print costs for similar posters would scale with area, so by the same logic they would rise by a factor of 2.25, not 1.5; recognising which factor (linear or squared) governs a quantity is the recurring skill this style of question is testing.
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