For a weekend sale, the shop owner hangs two similar triangular flags above the doorway. The smaller flag has sides of 18 cm, 24 cm and 30 cm. The largest s...
Question 1 Report
For a weekend sale, the shop owner hangs two similar triangular flags above the doorway. The smaller flag has sides of 18 cm, 24 cm and 30 cm. The largest side of the bigger flag is 45 cm.
- Find the scale factor from the smaller flag to the bigger flag. (1)
- Work out the perimeter of the bigger flag. (3)
Answer Details
This question tests identifying corresponding sides between similar triangles by matching the largest side to the largest side, then scaling the whole perimeter.
- The largest side of the smaller flag is 30 cm, and this corresponds to the largest side of the bigger flag, 45 cm. The scale factor is \(45 \div 30 = 1.5\). [1]
- The perimeter of the smaller flag is \(18 + 24 + 30 = 72\) cm. Since perimeter is a length, it scales by the same linear scale factor: \(72 \times 1.5 = 108\) cm. [3]
Exam tip: when a similar shape's sides are not labelled with matching letters, match sides by relative size (largest to largest, smallest to smallest) rather than by the order they are listed in the question.
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