If the width of the lawn is w and the dimensions of the rectangular museum are a and b, the area of the lawn is 60×80=4800-ab=0.4ab square metres.
So 4800=1.4ab. The dimensions of the ground area are a+2w and b+2w because the width w of the lawn is uniform.
a+2w=80, a=80-2w; b+2w=60, b=60-2w;
w=35±√(6175/7)=64.7m, 5.3m (approx).
We can reject 64.7m because this value would lead to negative values for a and b; therefore, a=80-10.6=69.4m, b=49.4m.
Area of museum (footprint)=3428.36m² approx.
Area of lawn=4800-3428.36=1371.64m² approx.
1371.64/3428.36=0.40 approx (40%).