a person 2m tall casts a shadow 1 m long when a building has a 6-m shadow. How high is the building?
any help would be greatly appreciated!
thank you
To determine the height of the building, you can set up a proportion comparing the heights of the person and the building to the lengths of their respective shadows.
Let's represent the height of the person as P and the height of the building as B.
We know that the height of the person is 2m, and the person's shadow is 1m long.
We also know that the building's shadow is 6m long.
To set up the proportion, we can write:
P / 1 = B / 6
Now, we can cross-multiply to solve for B:
1 * B = P * 6
B = (P * 6) / 1
B = 6P
Substituting the value we have for the height of the person:
B = 6 * 2
B = 12
Hence, the height of the building is 12 meters.
To solve this problem, we can use the concept of similar triangles. Similar triangles have proportional sides.
Let's set up the proportions:
Let 'x' be the height of the building.
2 meters (height of the person) corresponds to a shadow of 1 meter.
x meters (height of the building) corresponds to a shadow of 6 meters.
We can set up the proportion as follows:
2 / 1 = x / 6
To get the value of 'x', we need to solve for it.
Cross-multiplying the equation:
2 * 6 = 1 * x
12 = x
So, the height of the building is 12 meters.
Set up a ratio and cross multiply.
2/1 = x/6
x = 12