Discussion
A wire would enclose an area of 1936 m2, if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?
Answer: C
The closest sum is 1243 square metres.
A square of area 1936 m2 has side 44 m, so the wire is \(4 \times 44 = 176\) m long. Split in the ratio 3 : 1, the pieces are 132 m and 44 m.
\[ \begin{aligned} \text{square: side} &= 132/4 = 33,\ \text{area } 1089 \\ \text{circle: } 2\pi r &= 44 \\ \text{area} &= \frac{44^{2}}{4\pi} \approx 154 \\ \text{total} &\approx 1089 + 154 = 1243 \end{aligned} \]
2486 is exactly double the right answer. 1096 and 1111 are only a little more than the square on its own, so they leave out most of the circle's 154 m2.
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