the length and width of a rectangle have a sum of 70. what dimentions give the maximumarea?

To maximize the area you want the largest numbers possible to be added together, in order to do so, divided 70 by 2.

70/2 = 35

35 x 35 is the answer because it provides the maximum area.

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-08T10:56:12+02:00

A Length and width of 35 units each will give the maximum area of the rectangle.

Let us say the length of the rectangle is x

So, the width of the rectangle will be 70-x

What is the area of a rectangle?

The area of a rectangle with length l and width b is lb.

So, the area of the given rectangle A= x(70-x)

A(x) =x(70-x)

[tex]A(x) = 70x-x^{2}[/tex]

[tex]A'(x) = 70-2x[/tex]

[tex]A''(x) =-2(Negative)[/tex]

Since A"(x) is negative so from the second derivative test A'(x)=0 will give the maximum area.

[tex]A'(x)=0\\70-2x=0\\x=35[/tex]

So, x=35 will give the maximum area.

So, the length of the rectangle =35

Width of the rectangle =35

Therefore, A Length and width of 35 units each will give the maximum area of the rectangle.

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