A piece of molding 163 cm long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area
Answers
Given : A piece of molding 163 cm long is to be cut to form a rectangular picture frame.
To Find : What dimensions will enclose the largest area
Solution:
Let say Length = x
2 ( Length + Breadth ) = 163
=> 2 ( x + Breadth ) = 163
=> x + breadth = 163/2
=> breadth = 163/2 - x
Area = Length * Breadth
A= x ( 163/2 - x)
A = 163x/2 - x²
dA/dx = 163/2 - 2x
dA/dx = 0 => 163/2 - 2x = 0
=> x = 163/4
d²A/dx² = - 2 < 0 Hence minimum area
x = 163/4
breadth = 163/2 - x = 163/2 - 163/4 = 163/4
Length = Breadth = 163/4
163/4 x 163/4 dimensions will enclose the largest area
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