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A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3m, find how far she is away from the base of the pole.

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Answer : [9 m]

height of street light bulb = 6 m

woman's height = 1.5 m

woman's shadow = 3m

Let the distance between pole and women = x m

Here\ CD\parallel AB

In\ \Delta CDE and \Delta ABE

\angle E=\angle E  \text{(common angle)}

\angle ABE=\angle CDE  (\text{ each angle 90}^0)

\therefore \Delta CDE\sim \Delta ABE\text{ (by AA similarity criterion)}  

Then

\frac{ED}{EB}=\frac{CD}{AB}

\\\frac{3}{3+x}=\frac{1.5}{6}\\3 \times 6=1.5\left ( 3+x \right )\\18=4.5+1.5x\\18-4.5=1.5x

\\\frac{13.5}{1.5}=x\\9m=x

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