# Math

how could you find the measurements of the frame with a 16 inch perimeter antd the greatest possible area?

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1. A square of 4 by 4 would give you the largest area

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2. P=Perimeter

A=Area

a,b=sides of rectacangle

P=2a+2b

P=2(a+b) Divide with 2

P/2=a+b

a+b=P/2

a+b=16/2

a+b=8

b=8-a

A=a*b

A=a*(8-a)

A=8a-a^2

A=-a^2+8a

Function have extreme value in point where first derivative=0

First derivative:

dA/da=-2a+8

dA/da=0

-2a+8=0

8=2a Divide with 2

a=4in

b=8-a

b=8-4

b=4in

Second derivative:

d^2A/da^2=-2

When second derivative is negative tion have maximum.

a=4in b=4 in

A(max)=4*4

A(max)=16in^2

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