A wire length 4 meters is bent to form a rectangle. Find the measurement of its sides so that the rectangle has a maximum area.
Solution:
Perimeter:
2a+2b=4………(i)
a=(4-2b)/2
=2-b………(ii)
Luas:
A=ab………(iii)
Substitute (ii) into (iii)
=(2-b)b
=2b-b^2
Untuk dapatkan maximum area,
dA/db=2-2b
dA/db=0
2-2b=0
b=1
a=2-b
=2-1
=1
(d^2 A)/(db^2 )=-2
∴ maximum area with a=1,b=1.
