What is the area of quadrilateral ABCD?

✓ Correct Answer: Option C

(1) ABCD is a rectangle, Perimeter = 2(L+W) = 40. L+W=20. Not sufficient as L and W are unknown. (2) Diagonal AC = 15. In a rectangle, L^2 + W^2 = (diagonal)^2, so L^2 + W^2 = 15^2 = 225. Not sufficient alone. Together: We have L+W=20 and L^2+W^2=225. Squaring (L+W)=20 gives L^2+2LW+W^2=400. Substitute L^2+W^2=225: 225+2LW=400, so 2LW=175. Area = LW = 175/2 = 87.5. Sufficient.