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The bottom of the legs of a three legged...

The bottom of the legs of a three legged table are the vertices of an isosceles triangle with sides 5, 5 and 6. The legs are to be braced at the bottom by three wires in the shape of a Y. The minimum length of the wire needed for this purpose, is

A

`4+3 sqrt(3)`

B

`10`

C

`3+4 sqrt(3)`

D

`1+6sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A

`l = 4-x+2sqrt(9+x^(2))`
`(dl)/(dx) = -1 + (2)/(sqrt(9+x^(2)))`
`(dl)/(dx) = 0`
`implies x = sqrt(3)`
`(d^2 l)/(dx^2) = (18)/(sqrt(9+x^2)) gt 0`, for `x = sqrt(3)`
`:. l_("min") = 4-sqrt(3)+sqrt(9+3)`
`= 4+3sqrt(3)`.
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