An equilateral triangle ABC is formed by joining three rods of equal length and D is the mid-point of AB. The coefficient of linear expansion for AB is α₁ and for AC and BC is α₂. The relation between α₁ and α₂, if distance DC remains constant for small changes in temperature is

• A

  ${\mathrm{\alpha }}_1={\mathrm{\alpha }}_2$

• B

  ${\mathrm{\alpha }}_1=4{\mathrm{\alpha }}_2$

• C

  ${\mathrm{\alpha }}_2=4{\mathrm{\alpha }}_1$

• D

  ${\mathrm{\alpha }}_1=\frac{1}{2}{\mathrm{\alpha }}_2$