Discussion
The side of a square is 5 cm. How many times will the new area become, if the side of the square is doubled ?
Answer: D
The new area becomes 4 times the original.
The area of a square is the square of its side:
\[ \begin{aligned} \text{Original area} &= 5 \times 5 = 25\ \text{cm}^{2} \\ \text{New area} &= 10 \times 10 = 100\ \text{cm}^{2} \\ \frac{100}{25} &= 4 \end{aligned} \]
In general, doubling the side multiplies the area by \(2^{2} = 4\). The answer 2 times is the common error of thinking area grows in the same proportion as the side, and 8 times is what happens to the volume of a cube when its side is doubled.
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