a rectangle has an area of 64 inches2.a staright line is to be drawn from one corner of the rectangle to the mid point of one of the two more distant sides.what is the minimum posible length of such a line

Answer 1

I'll bet it's when the rectangle is a square, but let's proceed.

we can without loss of generality assume the rectangle's dimensions are 2 by 2x, where 2x is the long side.

The distance has two possible values:
√(4+x^2) or √(1+4x^2)
When x>=1, 4+x^2 <= 1+4x^2, so we know that the minimum distance will be

√(4+x^2)

That is, the shorter distance is from the corner to the opposite long side.

So, what is the minimum value of that? It is, naturally, when x=1, since we are assuming that 2x is the long side.

So, when x is 1, the dimensions are 2 by 2, and the rectangle is a square.

Scale up by a factor of 4, since our area is 64, and the rectangle is 8x8.

Answer 2

If two rectangles have 16 inches what are two possible areas for each rectangle