Question

A $5\text{m 60 cm}$ high vertical pole casts a shadow $3\text{m 20 cm}$ . Find at the same time the length of the shadow cast by another pole $10\text{m 50 cm}$ .

Answer 1

Here height of the pole and length of the shadow are in direct proportion .

Direct Proportion : Two quantities are said to be direct proportion if an increase in one leads to the increase in the other quantity and vice-versa .

We know that $1\text{m=100 cm}$ so

$5\text{m 60 cm = 5×100 +60 =500+60=560 cm}$

$3\text{m 20 cm =3×100+20=300+20=320 cm}$

$10\text{m 50 cm=10×100+50 = 1000+50=1050 cm}$

Let the length of the shadow of another pole be $\text{x}$ .

Since these two quantities are in direct proportion so

Height of the pole (in cm)	$560$	$1050$
Length of the pole (in cm)	$320$	$\text{x}$

So $\frac{560}{320}=\frac{1050}{\text{x}}$ , $\frac{320}{560}=\frac{\text{x}}{1050}$

$\text{x=}\frac{320}{560}\text{×1050=600 cm}$

Hence length of the shadow of the another pole is $600\text{cm}$