Question #341dd

Question

Question #341dd

1 Answer

Impact of this question

1899 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-29T05:21:25

A square of side 4cm

Explanation:

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

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

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

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

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

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

$\frac{d A}{d w} = 8 - 2 w = 0$ $(dA)/(dw) = 8-2w = 0$

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

Science

Math

Humanities

... and beyond

Question #341dd

1 Answer

Explanation:

Related questions

Impact of this question