Question

Nina was curious about the height of the Eiffel Tower. She used a 1.2 meter model of the tower and measured its shadow at 2 P.M. The length of the shadow was 0.9 meter. Then she measured the Eiffel Tower’s shadow, and it was 240 meters.

What is the height of the Eiffel Tower?

a.

.45

c.

30 m
b.

2880 m

d.

320 m

Answer 1

D. 320 meters

Explanation:

Answer 2

The height of the Eiffel Tower is 320 meters .

Option (d) is correct.

Explanation:

Let us assume that the height of the tower be x.

Let us assume that the shadow of the tower be y.

(As the shadow is always varies upon height .)

Thus

`x \propto y`

x =ky

`(x)/(y)= k`

As given

She used a 1.2 meter model of the tower and measured its shadow at 2 P.M.

The length of the shadow was 0.9 meter.

Here x = 1.2 meter

y = 0.9 meter

`(1.2)/(0.9)= k`

As given the Eiffel Tower’s shadow is 240 meters.

Here x = Height of Eiffel tower

y = 240 meters.

and

`(1.2)/(0.9)= k`

Put in the equation

`(x)/(y)= k`

`(Height\ of\ Eiffel\ Tower)/(240) = (1.2)/(0.9)`

`Height\ of\ Eiffel\ Tower = (1.2* 240)/(0.9)`

`Height\ of\ Eiffel\ Tower = (288)/(0.9)`

Simplify the above

Height of the Eiffel Tower = 320 meters .

Therefore the height of the Eiffel Tower is 320 meters .

Option (d) is correct.