MIN/MAX area of a rectangle inscribed in a rectangle

[nencho83]

http://bp3.blogger.com/_4Z2DKqKRYUc/Rnz_BgODzFI/AAAAAAAAAIw/uj_cVfPI8D4/s1600-h/Img_6-23-07_Blog.jpg

Could someone help me to understand how can I figure it out, how can I create a formula for finding min/max area of a rectangle inscribed in a rectangle, defined by given width and height. Also if it is possible to be inscribed a rectangle at all.

For a private case, when the rectangle is a square, it is pretty easy using the Pythagorean theorem, but for a common case I'm not sure if the inscribed rectangle is really inscribed.

 

[Hertz]

The maximum area is when the inside rectangle and the outside rectangle overlap and and have the same area. The minimum area is when all of the sides of the inside rectangle are length zero.

Is this your question?

 

[adjacent]

The maximum area is when the inside rectangle and the outside rectangle overlap and and have the same area. The minimum area is when all of the sides of the inside rectangle are length zero.

Is this your question?

When all the sides are zero length,then it is no longer a rectangle.It's just nothing.Smallest area is when you make the width,infinitely close to zero,(I mean,0.000000001,like this,you can write infinite zeros and then 1.)

 

[LCKurtz]

I assume that a rectangle is inscribed in another only all four vertices of the inscribed rectangle touch the outer rectangle. So the outer rectangle itself is the largest and there is either no minimum or a degenerate rectangle having area 0 for the min.

 

[CellCoree]

Hello,

Thank you for your question. I can definitely help you understand how to find the minimum and maximum areas of a rectangle inscribed in a rectangle.

First, let's define what it means for a rectangle to be inscribed in another rectangle. An inscribed rectangle is one that is contained within another shape, in this case a rectangle, with all four of its corners touching the sides of the larger rectangle. This means that the inscribed rectangle will have its sides parallel to the sides of the larger rectangle.

To find the minimum and maximum areas of a rectangle inscribed in a rectangle, we need to consider the different ways the inscribed rectangle can be oriented within the larger rectangle. The minimum area will occur when the inscribed rectangle is rotated so that its longer side is parallel to one of the sides of the larger rectangle. The maximum area will occur when the inscribed rectangle is rotated so that its shorter side is parallel to one of the sides of the larger rectangle.

To find the minimum and maximum areas, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's say the larger rectangle has a width of W and a height of H. To find the minimum area, we can set up the following equation:

Area of inscribed rectangle = length * width

= H * (W/2)

= HW/2

To find the maximum area, we can use a similar approach:

Area of inscribed rectangle = length * width

= (H/2) * W

= HW/2

So, the minimum and maximum areas of a rectangle inscribed in a rectangle with a width of W and a height of H are HW/2 and HW/2, respectively.

As for whether it is always possible to inscribe a rectangle in another rectangle, the answer is yes. As long as the dimensions of the larger rectangle are greater than or equal to the dimensions of the inscribed rectangle, it can be inscribed. However, the inscribed rectangle may not be a perfect rectangle, as its sides may not be exactly equal to the sides of the larger rectangle.

I hope this helps you understand how to find the minimum and maximum areas of a rectangle inscribed in a rectangle. Let me know if you have any further questions.