Two triangular flower beds on a garden allotment have the same shape. The smaller has sides 6 m, 8 m and 9 m; the longest side of the larger is 22.5 m. Find...
Question 1 Report
Two triangular flower beds on a garden allotment have the same shape. The smaller has sides 6 m, 8 m and 9 m; the longest side of the larger is 22.5 m.
- Find the shortest side of the larger bed. (2)
Answer Details
Similar shapes have all their corresponding lengths in the same ratio, so one matched pair of sides fixes the scale factor for every other pair.
- The longest side of the smaller bed is 9 m and the longest side of the larger is 22.5 m, so the scale factor is \(\frac{22.5}{9} = 2.5\). [1]
- The shortest side of the smaller bed is 6 m, so the shortest side of the larger is \(6 \times 2.5 = 15\) m. [1]
Match longest to longest and shortest to shortest, not sides in the order they happen to be listed. For completeness the middle side becomes \(8 \times 2.5 = 20\) m, and the larger bed has sides 15 m, 20 m and 22.5 m, still in the ratio \(6 : 8 : 9\).
The scale factor applies to lengths only. The larger bed's area is \(2.5^2 = 6.25\) times that of the smaller, not 2.5 times.
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