In rectangle ABCD, M is the midpoint of BC, Ma ⊥ MD. if the perimeter of rectangle is 48CM, the area of rectangle ABCD is______ cm2．

In rectangle ABCD, M is the midpoint of BC, Ma ⊥ MD. if the perimeter of rectangle is 48CM, the area of rectangle ABCD is______ cm2．

The area of rectangle ABCD is 128. The area of rectangle ABCD is 128

As shown in the figure, in the rectangular ABCD, M is the midpoint of BC, Ma ⊥ MD is made through M, the perpendicular foot is m, and the area of the rectangle is 128cm2

In △ ABM and △ DCM, ab = CD, B = C = 90 °, M is the middle point of BC, BM = cm. In △ ABM and △ DCM, ab = CD, B = CBM = cm, △ ABM ≌ DCM (SAS), am = DM, ≌ Ma ⊥ MD, ≌ mad = MDC = 45 °, ab = BM = 12bc, the area of ∫ rectangle is 128cm2, ≌ ab · 2Ab = 128, ≌ BC = 16, perimeter of rectangular ABCD = 2 (8 + 16) = 48