Answered

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Find the smallest perimeter and the dimensions for a rectangle with an area of 36 in squared.

Sagot :

okpalawalter8

Answer:

Therefore the smallest parameters is  (6,6) and a dimension of 24 inches

Step-by-step explanation:

From the question we are told that

area of dimension is  [tex]A=36[/tex]

Generally the perimeter of  rectangle is given as

      [tex]x,y=36[/tex]

Given by

      [tex](x,y)=2x+2y[/tex]

Mathematical solving for perimeter of rectangle

    [tex]x=\frac{36}{y}[/tex]

    [tex]f(y)= 2\frac{36}{2} +2y\\f(y)= \frac{72}{y} +2y[/tex]

Generally in finding minimum perimeter

     [tex]f'(y)=\frac{-72}{y^2} +2=0\\[/tex]

     [tex]y=6[/tex]

[tex]f(6,6)=2(6)+2(6) \\f(6,6)=24 inches[/tex]

Therefore the smallest parameters is  (6,6) and a dimension of 24 inches

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