Question 1109661: -find the longest stick that can be placed inside a rectangles with sides 4cm and 9cm?
-find the perimeter of the square with vertices A(2,3),B(-1,5),C(-5,1) & D(-1,-3)?
Answer by KMST(5399)   (Show Source):
You can put this solution on YOUR website! The longest stick that can be placed inside a rectangles with sides 4cm and 9cm
is a hair-thin stick as long as the diagonal of the rectangle.
According to the Pythagorean theorem, the length of that stick is
  .
That is approximately  .
The points A(2,3), B(-1,5), C(-5,1) & D(-1,-3), shown on the sketch below,
do not determine a square.
They are vertices of a quadrilateral with no parallel sides,
Points P(3,1), B(-1,5), C(-5,1) & D(-1,-3) are the vertices of a square,
with PC and BD being its diagonals.
They are equally long, perpendicular, and bisect each other,
and that tells us PBCD is a square.
The lengths of the sides of ABCD are
The perimeter of ABCD is approximately
 .
The exact result is
 .
If we use approximate side lengths with more decimal places,
we realize that the unrounded result is closer to 21.6:
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