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Mathematics · Triangles · NCERT Examples

Example 7

A complete, independently verified solution for NCERT Example 7.

Mathematics · Chapter 6 · NCERT Examples

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NCERT Example

Example 7

AA similarity · shadows · application

A girl of height 90 cm is walking away from the base of a lamp-post at 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

A lamp-post AB, a girl CD, and the shadow DE along the same ground line.
Figure 6-32 from the supplied NCERT chapter.

Solution

Board-exam working:

Let DE = x m be the girl's shadow after 4 seconds.

Distance walked, BD = 1.2 × 4 = 4.8 m. Therefore, BE = BD + DE = 4.8 + x metres.

AB = 3.6 m and CD = 90 cm = 0.9 m.

In △ABE and △CDE, ∠B = ∠D = 90° and ∠E is common. Therefore, △ABE ∼ △CDE by AA similarity.

The correspondence is A ↔ C, B ↔ D and E ↔ E. Hence:

BEDE=ABCD\frac{BE}{DE}=\frac{AB}{CD}
4.8+xx=3.60.9=4\frac{4.8+x}{x}=\frac{3.6}{0.9}=4
4.8+x=4x4.8+x=4x
4x−x=4.84x-x=4.8
3x=4.83x=4.8
x=1.6x=1.6

Final answer

The girl's shadow is 1.6 m long.