Question #341dd

1 Answer
Jack
Sep 29, 2016

A square of side 4cm

Explanation:

The rectangle in question will have perimeter P = 16
The perimeter of a rectangle is P = 2h + 2w where h and w are the height and width, respectively.

Combining equations, it is clear 16 = 2h+2w => h+w = 8

It is also useful to note, then that h = 8-w

We know the area of the rectangle is A = h*w

Substituting in our equation above, we can say:
A = (8-w)*w or A = 8w-w^2

Now we differentiate area with respect to the width and set the equation equal to 0 (notice that if we solved for height there would be no difference, since the sides are arbitrarily named).

(dA)/(dw) = 8-2w = 0

Solving, we see w = 4.
Since 8 = w+h, h = 4 as well.
Thus, our solution is a square with w=4 and h=4.

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