Question 120257: a 4-foot pole casts a shadow of 3 feet. how tall is a tree with a shadow of 6 feet. Found 2 solutions by checkley71, bucky:Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! You can solve this problem using a proportion. Let L equal the length of the object and
S equal the length of the corresponding shadow.
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Since the length of the pole is 4-feet and its corresponding shadow is 3 feet, we can set the
ratio of L (the pole length) to S (the corresponding shadow length) and get:
.
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For the tree, the ratio must be the same way ... that is the unknown length must be the numerator
and the corresponding shadow length of its shadow must be the denominator. So for the tree
the ratio of its length of the shadow length can be written as:
.
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We can now establish a proportion by setting these two ratios equal to get:
.
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One way to solve this is to make the denominators on both sides equal. You can do this
by multiplying the numerator and the denominator of the ratio on the left side by 2 to
get:
.
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This shows you that for these two ratios to be equal, since the denominators are equal, the
numerators must be equal also. Therefore, L must equal 8 which tells you that the tree
is 8 feet tall.
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Proportions can also be solved by cross multiplying ... multiply each numerator by the denominator
on the opposite side and set the two products equal. For this problem you start with the
proportion:
.
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Multiply the 4 times the 6 to get 24. Then multiply the L times the 3 to get 3L. Set the
two products equal and you have:
.
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Solve for L by dividing both sides of this equation by 3 and you have:
.
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This is the same answer as we got the other way ... the tree is 8 feet tall.
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Hope this helps you to understand the problem.
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