# A wire in the shape of Y is hanged from two points #A# and #B#, #8# feet apart. The lower end of wire reaches a point #10# feet from #AB#. What is the shortest possible length of the wire?

##### 2 Answers

Shortest length of wire that can be used is

#### Explanation:

The above can be better described by the following figure.

Now using Pythagoras theorem, if

and total length of wire is

This will be minimum when

As

or

or

and squaring we get

or

or

#=(60+-sqrt(3600-3408))/6=(60+-sqrt192)/6#

or

But

Hence

=

The shortest total length of the wire that can be used

#### Explanation:

Let the length of the perpedicular

The total height being 10ft the height of

Since in

Here

By pythagoras theorem

So total length of the wire

To know the minimum length of wire required we impose the condtion

So

Hence minimum length can be had by inserting