Discussion
Which one of the following has a greater perimeter than the rest?
Answer: C
Work out all four perimeters and compare.
Square, area 36: side \( \sqrt{36} = 6 \), so
\[ P = 4 \times 6 = 24 \text{ cm} \]
Equilateral triangle, side 9:
\[ P = 3 \times 9 = 27 \text{ cm} \]
Rectangle, length 10 and area 40: breadth \( \tfrac{40}{10} = 4 \), so
\[ P = 2(10 + 4) = 28 \text{ cm} \]
Circle, radius 4:
\[ C = 2\pi (4) = 25.13 \text{ cm} \]
The rectangle's 28 cm is the largest. It is also the least compact shape here, which is the general pattern: for a given area, the more elongated the figure, the longer its boundary - and the circle is always the most economical.
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