# Q9. 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 5m long.

Consider there is a direct proportion relation of pole height with pole shadow.

So we have  5m 60cm high verticle pole that casts a shadow of 3m 20cm long .

hence,

(i) for the length of the shadow cast by another pole of 10 m 50cm high would be 'x' cm;

$\frac{560cm}{320cm}=\frac{1050cm}{x}$

finding x from the equation we get;

$x=600cm$.

Therefore for a 10m 50cm pole we would get a shadow of 600cm or 6m length.

(ii) The height of a pole which casts a shadow of 5m long let it be 'y'

similar relation holds here also, so we can apply it once more

$\frac{560cm}{320cm}=\frac{y}{500cm}$,

we get  $y=875cm\ or\ 8m\ 75cm$.

Thus, the height of a pole which casts a shadow of 5m long is 8m 75cm.

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