Along the fence bordering the school sports field, flag A and flag B are strung up together as mathematically similar triangular pennants for the whole day....
Question 1 Report
Along the fence bordering the school sports field, flag A and flag B are strung up together as mathematically similar triangular pennants for the whole day. Flag A measures 18 cm along its base and reaches 24 cm from base to tip, as shown. Flag B's base measures 27 cm.
- Find the height of flag B. (2)
- Work out the area of flag B. (2)
Answer Details
This question tests similar triangles: the scale factor found from one pair of corresponding sides converts every other length, and the area is then found from the two scaled dimensions.
- The bases 18 cm and 27 cm are corresponding sides, giving a scale factor of \(27 \div 18 = 1.5\). The height of flag B is \(24 \times 1.5 = \) 36 cm [2].
- The area of flag B is \(\frac{1}{2} \times 27 \times 36 = \) 486 cm² [2].
Since the base and height of flag B are now both known exactly, its area is calculated directly rather than by squaring the 1.5 scale factor and applying it to flag A's area, though both routes agree: flag A's area is \(\frac{1}{2} \times 18 \times 24 = 216\) cm\(^2\), and \(216 \times 1.5^2 = 486\) cm\(^2\).
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