Question 46407
You can start by writing the equation of proportionality:
{{{P = k*sqrt(L)}}} Where: P = period, L = Length, and k is the constant of proportionality.
We need to find the value of k.  We can do this by substituting the given values of L (6 ft) and P (2 secs) into the above formula and solving for k.

{{{2 = k*sqrt(6)}}} Divide both sides by {{{sqrt(6)}}}
{{{k = 2/sqrt(6)}}}

Now the formula for the period is:
{{{P = (2/sqrt(6))sqrt(L)}}}

To answer your probem however, we need to solve this equation for L.
{{{P = (2/sqrt(6))sqrt(L)}}} Multiply both sides by {{{sqrt(6)}}} and divide by 2.
{{{sqrt(6)P/2 = sqrt(L)}}} Now square both sides.
{{{(6/4)P^2 = L}}} Simplify.
{{{L = (3/2)P^2}}}

Now we can answer your problem. What should L be if P is to be 1 second.
Just substitute P = 1 into the above equation and solve for L.
{{{L = (3/2)(1^2)}}}
{{{L = 3/2}}}
{{{L = 1.5}}}ft.