Question

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time -
(i) the length of the shadow cast by another pole 10 m 50 cm high
(ii) the height of a pole which casts a shadow 5 m long.

Answer 1

(i) Let the length of the shadow of the other pole be x m. 
1 m = 100 cm 
The given information in the form of a table is as follows.

Height of pole (in m)	5.60	10.50
Length of shadow (in m)	3.20	x

More the height of an object, more will be the length of its shadow. 
Thus, the height of an object and length of its shadow are directly proportional to each other. 
Therefore, we obtain.
\(\frac{5.60}{3.20}=\frac{10.50}{x}\)

\(⇒ x = \frac{10.50\times3.20}{5.60}=6\)
Hence, the length of the shadow will be 6 m.

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(ii) Let the height of the pole be y m. 
The given information in the form of a table is as follows.

Height of pole (in m)	5.60	y
Length of shadow (in m)	3.20	5

The height of the pole and the length of the shadow are directly proportional to each other. 
Therefore,
\(\frac{5.60}{3.20}=\frac{y}{5}\)

\(y=\frac{5\times5.60}{3.20}=8.75\)
Thus, the height of the pole is 8.75 m or 8 m 75 cm.