As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1·2 m/s. If the lamp is 3·6 m above the ground, find the length of her shadow after 4 seconds.
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
Given: Height of lamp post AB = 3.6 m, Height of girl CD = 90 cm = 0.9 m, Speed = 1.2 m/s, Time = 4 s.
Let DE = shadow length = $x$ m.
Distance walked in 4 s:
$$BD = 1.2 \times 4 = 4.8 \text{ m}$$
In △ABE and △CDE:
$\angle B = \angle D = 90°$ (both are vertical to the ground)
$\angle E = \angle E$ (common angle)
∴ △ABE ~ △CDE (AA similarity criterion)
Therefore:
$$\frac{BE}{DE} = \frac{AB}{CD}$$
$$\frac{4.8 + x}{x} = \frac{3.6}{0.9} = 4$$
$$4.8 + x = 4x$$
$$3x = 4.8$$
$$x = 1.6 \text{ m}$$
∴ The length of the girl's shadow after 4 seconds is 1.6 m.
Source: Chapter 6, Section 6.4 (Example 7)
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Explanation
- Key concept: AA similarity — when two angles of one triangle equal two angles of another, the triangles are similar and corresponding sides are proportional.
- Common mistake: Forgetting to convert 90 cm to 0.9 m before setting up the ratio.
- Setup: BE = BD + DE = 4.8 + x (total base), not just 4.8.
- Examiners expect you to state the similarity criterion explicitly (AA) and show both the angle equalities before writing the proportion.