A phone company's triangular logo has sides of length \(5\) cm, \(7\) cm and \(9\) cm. For a shop sign, the logo is enlarged to a mathematically similar tri...
Question 1 Report
A phone company's triangular logo has sides of length \(5\) cm, \(7\) cm and \(9\) cm. For a shop sign, the logo is enlarged to a mathematically similar triangle whose longest side is \(27\) cm, as shown.
- Find the scale factor of the enlargement. (1)
- Work out the length \(x\), the shortest side of the sign. (2)
Answer Details
Because the sign is a mathematically similar enlargement of the logo, its sides share one common scale factor with the logo's corresponding sides; comparing the two longest sides finds that factor, which then applies to the shortest side as well.
(a) The longest sides, \(9\) cm and \(27\) cm, correspond, so the scale factor is \(27\div9=3\). [1 mark]
(b) The shortest side of the logo, \(5\) cm, scales by the same factor: \(x=5\times3=15\) cm. [2 marks]
Matching the longest side of the logo to the longest side of the sign to find the scale factor, rather than assuming which sides correspond, is essential when a shape has three different side lengths, since the correspondence must follow the relative sizes, not the order the lengths are listed in.
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