Question

A building casts a shadow 30 m long. At the same time, the shadow cast by a 41-cm tall pole is 72 cm long. Find the height of the building.

Answer 1

The height of the building is 17.08 m.

Explanation:

Let the height of the building be h.

The building casts a shadow 30 m long. So, the ratio of object and its shadow is

`r_1=(x)/(30)`

At the same time the shadow cast by a 41-cm tall pole is 72 cm long. So, the ratio of object and its shadow is

`r_2=(41)/(72)`

The ratio of object and its shadow is same at a point of time.

`r_1=r_2`

`(x)/(30)=(41)/(72)`

On cross multiplication we get

`72x=30* 41`

`72x=1230`

Divide both sides by 72.

`x=(1230)/(72)`

`x=17.0833\approx 17.08`

Therefore the height of the building is 17.08 m.

Answer 2

In this question, it is given that

A building casts a shadow 30 m long. At the same time, the shadow cast by a 41-cm tall pole is 72 cm long.

Let the height of the building be x m.

Now we set the ratio, which is

`(x)/(3000)= (41)/(72)`

Cross multiplication

`72x = 3000*41 \\ 72x = 123000`

Dividing both sides by 72

`x = (123000)/(72) = 1708.33 cm= 17 m`