- A flag staff 17.5m high casts a shadow of length 40.25m.

- The height of the building which casts a shadow of length 28.75m can be figure out in this way.

## Explanation

Two given entities here are

- Height
- Shadow

To determine the relation here, let suppose; the height of the building which casts a shadow of length 28.75m = y

__Case__

As we know that;

Shadow Height

40.25m 17.5m

28.75 y

- Shadow increases as height increased.
- Shadow decreases as the height decreased.

This clearly indicates that there is direct relation.

Direct/Indirect relation tells how the equation will be written.

40.25 : 28.75 :: 17.5 : y ________ (A)

After simplifying equation (A), we can easily figure out the value of y (y = 12.5m)

## To Find

The height of the building which casts a shadow of length 28.75m = ?

## Solution

__Method I__

Let suppose

The height of the building which casts a shadow of length 28.75m = y

Shadow Height

40.25m 17.5m

28.75 y

Relation between shadow and height is direct, so;

40.25 : 28.75 :: 17.5 : y

40.25 x y = 28.75x 17.5

40.25y = 503.125

y = 503.125/40.25

y = 12.5

**The height of the building which casts a shadow of length 28.75m = 12.5m**

__Method II__

40.25m shadow is casted by a flag of height = 17.5m

1m shadow is casted by a flag of height = 17.5/40.25

1m shadow is casted by a flag of height = 0.435m

28.75m shadow is casted by a building of height = 0.435 x 28.75

28.75m shadow is casted by a building of height = 12.5m

**The height of the building which casts a shadow of length 28.75m = 12.5m**

## Conclusion

A flag staff 17.5m high casts a shadow of length 40.25m. The height of the building which casts a shadow of length 28.75m under similar condition will be 12.5m.