# Proportions

• May 9th 2009, 10:11 AM
ambergarrett955
Proportions
Hey! Could use a little help on how to set up this proportion. I know that the height of the tree = x but I'm not sure where 2x+4 should be put or if that is even right, here is the question:

At a point on the ground 60 ft. from the base of the tree, the distance to the top of the tree is 4 ft. more than 2 times the height of the tree. Find the height of the tree.

Any help is appreciated---just need help on setting up the proportion. Not solving all the way. Thanks.
• May 9th 2009, 10:18 AM
VonNemo19
here ya go!
This is easy let the hieght of the tree be x, therefore, the distance from the top of the tree to the point on the ground 60 feet away from the base of the tree ( the hypotenuse) is 2x+4. So, by the pythagorean relationship, we have

$(2x+4)^2-x^2=(60)^2$

can you take it from here?
• May 9th 2009, 10:19 AM
galactus
Let the height of the tree be h.

The hypoteneuse of the triangle formed is given as 2h+4. You had that right.

The height of the tree is then:

$h=\sqrt{(2h+4)^{2}-3600}$

solve for h.

It is a nice integer.
• May 9th 2009, 10:20 AM
VonNemo19
By the way, this is not a proportion problem. There is no other "triangle" given for which this one is proportional to.

You know what I mean.
• May 9th 2009, 10:33 AM
ambergarrett955
Thanks. I realize that now. Sorry for the confusion.
• May 9th 2009, 10:51 AM
VonNemo19
Quote:

Originally Posted by ambergarrett955
Thanks. I realize that now. Sorry for the confusion.

It's cool man. We live and we learn. Peace Out.(Hi)