Three rods of equal of length are joined to from an equilateral triangle ABC. `D` is the midpoint of AB. The coefficient of linear expansion is `alpha_(1)` for AB and `alpha_(2)` for `AC` and `BC` . If the distance `DC` remains constant for small changes in temperature,

Explanation

`cos 60^(@)=(l_(1)^(2)+l_(2)^(2)-l_(2)^(2))/(2l_(2)l_(2))=(l_(1))/(2l_(2))`
`(1)/(2)=(l(1+alpha_(1)Deltatheta))/(2l(1+alpha_(2)Deltatheta))`
`alpha_(1)=alpha_(2)rArr(alpha_(1))/(alpha_(2))=1`