Question

A water tank cast a Shadow 21m long . A tree of height 9.5 m cast a shadow 8m long at the same time. The heights of the shadow are directly proportional to their heights finfld the height of tank

Answer 1

Given:

Length of shadow of water tank = 21 m

Height of tree = 9.5 m

Length of shadow of tree = 8 m

The Heights of the shadows are directly proportional to their heights.

To find:

Height of tank = ?

Solution:

First of all, let us learn the meaning of directly proportional.

A quantity is terms as directly proportional to other quantity, if increase in one quantity results in increase of the other

AND

decrease in one quantity results in decrease of the other quantity.

Here, we are given that height of shadow is directly proportional to actual height.

Let height of shadow be represented by $h_s$

actual height be represented by $h$

i.e. $h_s \propto h$

In other words:

$\dfrac{h_s(tank)}{h_s(tree)} = \dfrac{h(tank)}{h(tree)}$

Putting the given values:

$\dfrac{h_s(tank)}{8} = \dfrac{21}{9.5}\\\Rightarrow h_s(tank) = \dfrac{21}{9.5} \times 8\\\Rightarrow \bold{h_s(tank) = 17.68\ m}$

So, the answer is 17.68 m