Correct Answer - C
The distance between the apex and the midpoint of the base, using Pythagoras theorem `l=sqrt((l_2)^(2)=((l_(1))/(2))^(2))`
or, `l^(2) = (l_2)^(2) = ((l_1)/(2))^(2)`.
Differentiating (i) w.r.t. Temperature
`0=2l_(2) xx(dl_2)/(dT) -2((l_1)/(2)) * 1/2 xx (dl_(1))/(dt)`
`(l_1)/(2) xx l_(1) alpha_(1) = 2l_(2)alpha_(2)`
`((l_1)/(l_2))^(2) = 4 (alpha_2)/(alpha_1) rArr (l_1)/(l_2) = 2sqrt((alpha_2)/(alpha_1))`.