✔ 最佳答案
let w be the width of the rectangle
then the length is √[(2a)^2 -w^2]
=√(4a^2 -w^2)
area of the rectangle
A= w*√(4a^2 -w^2)
Differentiate w.r.t. w
dA/dw = √(4a^2 -w^2) + (1/2)(-2w^2)/√(4a^2 -w^2)
= √(4a^2 -w^2) + (-w^2)/√(4a^2 -w^2)
=[ (4a^2 -w^2 -w^2)]/√(4a^2 -w^2)
=[ (4a^2 -2w^2)]/√(4a^2 -w^2)
put dA/dw = 0
[ (4a^2 -2w^2)]/√(4a^2 -w^2) =0
4a^2 -2w^2=0
2w^2 =4a^2
w =(√2)a
length =√(4a^2 -w^2)
=(√2)a
area =(√2)a*(√2)a
=2a^2