let r be the radius of the island, then
(r+40) is the radius of the complete territory:
75% = (3/4) (for affirmation only )
(3/4) * π * (r+40)ē = π * rē
Expand the LHS and collect all terms on the LHS. You'll get:
-(1/4)πrē + 60πr + 1200 = 0 . Divide by -(1/4)π
rē - 240r - 4800 = 0.
r ≈ 258.564 or r ≈ -18.564 The negative solution doesn't make much sense here.
Area of the island: A(r) = π * rē that means: A(258.564) ≈ 210,032 kmē