The formula that relates period, T, to length, L is

#T = 2*pi*sqrt(L/g)#

Let the original period and length be #T_1 and L_1# respectively. Therefore in the original configuration,

#T_1 = 2*pi*sqrt(L_1/g)" "# Eq(1)

After the length is increased, the formula looks like this

#1.5*T_1 = 2*pi*sqrt((L_1+0.6 m)/g)#

Rearranging the formula

#sqrt((L_1+0.6 m)/g) = (1.5*T_1)/(2*pi) = 0.239 * T_1#

Squaring both sides

#(L_1+0.6 m)/g = 0.057*T_1^2#

Working to get L_1 by itself

#L_1/g + 0.6 m/g = 0.057*T_1^2#

#L_1/g = 0.057*T_1^2 - 0.6 m/g#

#L_1 = (0.057*T_1^2 - 0.6 m/g)*g#

#L_1 = 0.057*g*T_1^2 - 0.6 m " "#Eq(2)

Now we will substitute the expression for #T_1# from Eq(1) in for the #T_1# from Eq(2).

#L_1 = 0.057*g*(2*pi*sqrt(L_1/g))^2 - 0.6 m#

Working to simplify that

#L_1 = 0.057*cancel(g)*(2*pi)^2*(L_1/cancel(g)) - 0.6 m#

#L_1 = 0.057*(2*pi)^2*(L_1) - 0.6 m#

#L_1 = 2.25*L_1 - 0.6 m#

Getting close now.

#1.25L_1 = 0.6 m#

#L_1 = (0.6 m)/1.25 = 0.48 m#

I hope this helps,

Steve