Maxima Problem (1 Viewer)

[Carly_57]

A piece of wire of length 120cm is bent to form a rectangle. Find the dimesions of the rectangle is the area is to be a maximum.

I have no idea where to go with this one. Thanks

 

[Riviet]

Let the width and breadth of rectangle be a and b.
2a+2b=120
a+b=60
b=60-a *
Area=ab
=a(60-a)
=60a-a²
d/dx(60a-a²)=60-2a=0
2a=60
a=30
.'. b=60-30
=30
.'. dimensions of rectangle that make area a max are 30cm by 30cm.

 

[pLuvia]

You should know that for maximum area of a rectangle the sides are equal. So the maximum area would be a square