Discussion
A wire in the form of a square encloses an area of 144 cm2. How much area is enclosed if the same wire is bent in the form of a rectangle of length 16 cm ?
Answer: C
The rectangle encloses 128 cm2.
The wire's length stays the same; it is the perimeter of both shapes.
\[ \begin{aligned} \text{side} &= \sqrt{144} = 12\ \text{cm} \\ \text{wire} &= 4 \times 12 = 48\ \text{cm} \\ 2(16 + b) &= 48,\ b = 8\ \text{cm} \\ \text{area} &= 16 \times 8 = 128\ \text{cm}^{2} \end{aligned} \]
The option 48 cm2 is the wire's length in centimetres, not an area, and 124 and 96 do not come from a 16 cm by 8 cm rectangle. As expected, the rectangle encloses less than the square of the same perimeter.
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