Two similar triangular set-square rulers, sold together as a matching pair by a stationery shop for use in geometry lessons, have corresponding sides in the...
Question 1 Report
Two similar triangular set-square rulers, sold together as a matching pair by a stationery shop for use in geometry lessons, have corresponding sides in the ratio \(2 : 5\). The smaller set-square has a perimeter of 24 cm. Work out the perimeter of the larger set-square. (3)
Answer Details
For similar shapes, perimeter is a length (a 1-dimensional quantity), so it scales by exactly the same linear scale factor as any individual side.
The ratio of corresponding sides, \(2:5\), gives a scale factor from the smaller to the larger set-square of
\[5\div2=2.5\] [1 mark]Since perimeter is built entirely from lengths, it scales by this same linear factor, not by its square (which is only for area) or its cube (which is only for volume). [1 mark]
Applying the factor to the smaller perimeter:
\[24\times2.5=60 \text{ cm}\] [1 mark]Recognising that perimeter behaves like a length, not an area, is the key idea: multiplying by \(2.5\) directly (rather than \(2.5^{2}=6.25\)) is what similarity rules require for any 1-dimensional measurement.
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