Question

A vertical pole of length 7.5 m casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.

Answer 1

36meter

Step-by-step explanation:

proportionally it can be said

7.5:5=15:10=3:2

By the rule it can be expressed as a proportion

3:2::x:24

24×3=2x

72=2x

x=72/2

x=36

the pole is 36 meters tall.

Answer 2

As we know that vertical pole of length 7.5 m casts a shadow 5m long on the ground.

~From this reference, we can derive that how much height of pole will make shadow of 1 m as:-

$\colon\mapsto{\sf{ Height_{(shadow)} = Height_{(Pole)} }} \\ \\ \colon\mapsto{\sf{ 5m = 7.5m }} \\ \\ \colon\mapsto{\sf{ \cancel{ \dfrac{7.5}{5} } }} \\ \\ \colon\mapsto{\sf{ 1.5 m }}$

So, we found that 1.5m of Pole will make shadow of 1m.

~Now, According to above reference we also can find Height of the tower as:- we know that 1.5m of object makes shadow of 1m so,

$\colon\mapsto{\sf{ 24 \times 1.5 }} \\ \\ \colon\mapsto{\sf\pink{ 36 \ m }}$

Hence,

The height of the tower will be 36 m.