Question

Question #341dd

Answer 1

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`.