An isosceles triangles is formed with a thin rod of length `l_(1)` and coefficient of linear expansion `alpha_(1)`, as the base and two thin rods each of length `l_(2)` and coefficient of linear expansion `alpha_(2)` as the two sides. The distance between the apex and the midpoint of the base remain unchanged as the temperature is varied. the ratio of lengths `(l_(1))/(l_(2))` is

Explanation

`l = sqrt(((l_(1))/(2))^(2) +(l_(2))^(2))`
`l^(2) = ((l_(1))/(2))^(2) +(l_(2))^(2)`
`0 = (2l_(1))/(2)(1)/(2)(dl_(1))/(dT) +2l_(2) xx (dl_(2))/(dT)`
`l_(1) xx (l_(1)alpha_(1))/(2) xx DeltaT = 2l_(2) xx l_(2) alpha_(2) DeltaT`
`rArr (l_(1)^(2))/(l_(2)^(2)) =4 (alpha_(2))/(alpha_(1)) rArr (l_(1))/(l_(2)) = 2 sqrt((alpha_(2))/(alpha_(1)))`.