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 AB = x
AF = FE = x
BC = CD = 2x
ED = x
A = 3x^2
P = 8x
3x^2 - 8x - 60 = 0
(3x + 10) (x - 6) = 0
x = 6
AC = (6^2 + 12 ^2)^½ = 180^½ = 6 x 5^½ = 13.42

Posted by retiarius on 2003-10-10 08:00:44