SOLUTION: The shadow of a building is 280 feet long. At the same time, a 5 foot tall boy's shadow is 2 feet long. How tall is the building? Please show me how to work out this problem.

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Question 253033: The shadow of a building is 280 feet long. At the same time, a 5 foot tall boy's shadow is 2 feet long. How tall is the building? Please show me how to work out this problem.
Found 2 solutions by richwmiller, Sunsensor:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We have two similar triangles which means their sides are proportional.
so we have
280/2=x/5
We are relating the shadow's to the heights.
So solve for x and you have the height of the building.
To solve for x you could
a) cross multiply (Some teachers frown on that method -because it isn't as solid pedagogically (as a teaching method) as the other two methods. You can't really see the reason why it works since you are not doing the same thing to both sides)
b) multiply each side by 5 then by 2
c) multiply both sides by 10

Answer by Sunsensor(1) About Me  (Show Source):
You can put this solution on YOUR website!
There is a guide for problem solving called Occam's Razor. The general concept is that among competing hypotheses, the method requiring the fewest set of assumptions is usually the best way to solve the problem. There are several ways to solve the problem of establishing the height of the building. In addition to an algebraic problem it can also be considered using Occam's Razor as a thought problem. This we know:
1. The shadow of the building is 280 feet long.
2. The shadow of a 5 foot boy (standing nearby) is 2 feet long.
So how high is the building? It is easiest to break down numbers into their basic units; here we are dealing with a basic unit of 1 foot. So let's shrink the boy down so that his shadow is 1 foot long. That means the boy is 2 1/2 feet tall. If a shadow of 1 foot results in a height of 2 1/2 feet, then a shadow of 280 feet results in a height of X feet. So 2 1/2 times 280 is....
Search the WEB for Occam's Razor. You will find the concept helpful with future problems.