he rectangular plate shown in Figure P19.55 has an area Ai equal to . If the temperature increases by T, each dimension increases according to the equation L = Li T, where  is the average coefficient of linear expansion. Show that the increase in area is
A = 2Ai T. What approximation does this expression assume?

Question

he rectangular plate shown in Figure P19.55 has an area Ai equal to   . If the temperature increases by  T, each dimension increases according to the equation  L = Li  T, where  is the average coefficient of linear expansion.  Show that the increase in area is 
 A = 2Ai  T.  What approximation does this expression assume?

anonymous · Answer

Consider a square(even a rectangle works). The increased length can be found out by the formula mentioned.
Now,area = side^2.
You will get the result,with a approximation that you neglect a term.