Look at this shape:
Assume AB = AF = FE = ED and BC = CD, and all the angles in the shape are 90 degrees.
Let A be the area of this shape (in cm^2), and P  the perimeter of this shape (in cm).
If A  P is 60, what is the length of line AC?
Let x be the length AB, AF, etc.
Then, the perimeter P = 8x, and the area of the figure A = 3x².
A  P = 60
3x²  8x = 60
3x²  8x  60 = 0
(3x + 10)(x  6) = 0
x = 6, 10.
Obviously, the distance in question must be positive, so x= 60.
Then, AC is the hypotenuse of a right triangle with legs 6 and 12.
Thus, AC² = 6² + 12²
AC = √180
AC = 6√5
AC ~= 13.4164

Posted by DJ
on 20031010 09:20:37 