SOLUTION: A tree casts a shadow 7.5 ft long at the same time that a woman 5 ft tall casts a shadow 3 ft long. How tall is the tree?

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Question 769005: A tree casts a shadow 7.5 ft long at the same time that a woman 5 ft tall casts a shadow 3 ft long. How tall is the tree?
Found 2 solutions by Edwin McCravy, 2897696:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
TAKE your pick of these:

1.  TREE'S HEIGHT over TREE'S SHADOW equals WOMAN'S HEIGHT over WOMAN'S SHADOW
2.  TREE'S HEIGHT over WOMAN'S HEIGHT equals TREE'S SHADOW over WOMAN'S SHADOW

or some other ways as long as you pair them up by 'height', or pair them up by
'shadow'.  {But don't get them criss-crossed)

Let TREE's HEIGHT = t.

A tree casts a shadow 7.5 ft long
 TREE'S SHADOW = 7.5

at the same time that
a woman 5 ft tall
WOMAN'S HEIGHT = 5

casts a shadow 3 ft long.
WOMAN'S SHADOW = 3


So if you use

1.  TREE'S HEIGHT over TREE'S SHADOW equals WOMAN'S HEIGHT over WOMAN'S SHADOW

 t%2F7.5%22%22=%22%225%2F3,  cross-multiply:
 3t = 37.5
  t = 12.5

or if you use

2.  TREE'S HEIGHT over WOMAN'S HEIGHT equals TREE'S SHADOW over WOMAN'S SHADOW


 t%2F5%22%22=%22%227.5%2F3      cross-multiply
 3t = 37.5
  t = 12.5 

Either way, the tree is 12.5 feet tall.    


Edwin

Answer by 2897696(96) About Me  (Show Source):
You can put this solution on YOUR website!
make a proportion(tree height ==woman height)/(tree shadow length==woman shadow)
x(since do not know how tall tree is)=5
--------------------------------------- ==> (x/7.5)=(5/3)
7.5>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>=3
now cross multiply:
3x=37.5
--=----
3 = 3
x=12.5
ANSWER: The tree is 12.5ft