9. According to a headline 'Glaciers in the French Alps have lost a quarter of their area in the past 40 years'.
What is the approximate percentage reduction in the length of the side of a square when it loses one quarter of its area, thereby becoming a smaller square?
A $13 \%$
B $25 \%$
C $38 \%$
D $50 \%$
E $65 \%$
SolUTION
A Suppose that a square of side length 1 , and hence area 1, has side length $x$ when it loses one quarter of its area. Then $x^{2}=\frac{3}{4}$ and so $x=\frac{\sqrt{3}}{2}$. Now $1.7^{2}=2.89$ and so $1.7<\sqrt{3}$. Hence $0.85<\frac{\sqrt{3}}{2}$. So the length of the side of the smaller square is at least $85 \%$ of its original value. Therefore the reduction in its length is less than $15 \%$. So, of the given options, it must be that $13 \%$ is correct.