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A girl of height $0.9\text{ m}$ is standing so that her distance from a lamp-post is $4.8\text{ m}$. If the lamp-post is $3.6\text{ m}$ high, what is the length of her shadow? 
A$1.2\text{ m}$
B$1.4\text{ m}$
C$1.6\text{ m}$
D$2.0\text{ m}$
Answer & Solution
Correct answer: C. $1.6\text{ m}$
The principle is that the large triangle formed by the lamp-post and its light ray is similar to the smaller triangle formed by the girl and her shadow.
1. Let the shadow length be $x$ m. Then the total distance from the lamp-post to the tip of the shadow is $4.8+x$.
2. By similarity of $\triangle ABE$ and $\triangle CDE$, $$\frac{BE}{DE}=\frac{AB}{CD}$$ so $$\frac{4.8+x}{x}=\frac{3.6}{0.9}=4.$$
3. Hence $4.8+x=4x$, so $3x=4.8$, giving $x=1.6$.
Option A and B come from incorrect algebra, while D would overestimate the shadow by not using proportional triangles correctly.
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