A tower casts a shadow of 16m at the same time that a 2.5m post cast a shadow of 4m. How high is the tower?
A simple ratio will do it:
h/16 = 2.5/4
solve for h
2.5/4 = x/16
Cross multiply and solve for x.
To find the height of the tower, we can use the concept of similar triangles. Let's assume the height of the tower is 'h' meters.
According to the given information:
The height of the post is 2.5m, and its shadow is 4m.
The height of the tower is 'h' meters, and its shadow is 16m.
Since the shadows are proportional to the heights, we can set up the following ratio:
(height of the post) / (shadow of the post) = (height of the tower) / (shadow of the tower)
Or, in equation form:
2.5 / 4 = h / 16
Now, let's solve for 'h':
2.5 * 16 = 4 * h
40 = 4h
Divide both sides of the equation by 4:
40 / 4 = h
10 = h
Therefore, the height of the tower is 10 meters.
To find the height of the tower, we can use a proportion.
First, let's assign variables to the given information.
Let h represent the height of the tower.
Let x represent the height of the post (2.5m).
We're given that the shadow of the tower (16m) is proportional to the shadow of the post (4m).
So we have the proportion:
h/16 = x/4
To solve for h, we can cross-multiply and then solve for h:
4h = 16 * 2.5
4h = 40
h = 40/4
h = 10
Therefore, the height of the tower is 10 meters.