To have a minimum perimeter the area needs to be a square
so a0 = sqrt 256 = 16 yards
and a1 = 16 yards
Remark
When you have two parallel lines cutting the sides of a triangle and one of them is the base of the triangle, then the 2 sides cut form a proportion. The safest way to handle this is to set up the proportion so that you are talking about sides of similar triangles..
Givens
BD || AE
CD = 16
CE = 16 + 4
CB = 12
CA = 12 + x
Set Up the Proportion
CD/CE = CB / CA
Substitute and Solve
16/20 = 12/(12 + x) Cross multiply
16*(12 + x) = 20 * 12 Combine the right
16*(12 + x) = 240 Remove the brackets.
192 + 16x = 240 Subtract 192 from both sides.
16x = 240 - 192
16x = 48 Divide by 16
x = 48 / 16
x = 3
