Question

a 5m 60cm high vertical pole casts a shallow 3m 20cm long. Find at the same time (i) the length of Shadow cast by another 10m 50cm high

Answer 1

Hi there !!
The following question is of the topic direct and inverse proportions

Given,

Height of the pole = 5m 60cm = 5.60 m
Length of the Shadow casted by it = 3m20cm = 3.20cm

(i)
To find the length of Shadow casted by another pole 10m 50cm high

10m 50cm can be written as 10.50 m

Let x be the height of the object
y be the length of the Shadow casted by it


$x \: \: \: \: \: \: \: \: \: \: \: 5.6 \: \: \: \: \: 10.50\\ \\ y \: \: \: \: \: \: \: \: \: \: 3.20 \: \: \: \: \: \: \: y2$
Here,
as the height of the object increases, the length of the Shadow also increases .

So, x is directly proportional to y

in this case,

$\frac{x1}{y1} = \frac{x2}{y2}$

$\frac{5.60}{3.20} = \frac{10.50}{y2}$

$\frac{10.50 \times 3.20}{5.60} = y2$

y2 = 6

Thus,

the length of Shadow is 6m