Calculating Area of Thermal Expansion for Non-Isotropic Materials

[vkt420]

Homework Statement

A non-isotropic material is heated, fractional increase in length is different along different directions. With length l₁=6.1 cm and l₂=6.0 cm. In direction of l₁, the coefficient expansion is $\alpha$₁= 10×10^-5 K^-1 and direction l₂ is $\alpha$₂= 40×10^-5K^-1. The plate is heated until it becomes a perfect square. What is the area of the square? (The answer is 38 cm²) I just don't know how use the equations without a given temperature.

Homework Equations

ΔL=$\alpha$L₀T
L_x=L_x0+L_x0$\alpha$ΔT
L_y=L_y0+L_y0$\alpha$ΔT
A₀=L_x0L_y0
A=L_xL_y

The Attempt at a Solution

Not sure what to do with the equations without the temperature.

 

[voko]

You need to find the temperature from the condition that the rectangular becomes square.