The perimeter of square =4a Perimeter of rectangle =2(1+b) Area of square =a2 Area of rectangle =1×b
Let the side of the square be a and the length and breadth of the rectangle be 1 and b respectively. The perimeter of a square = perimeter of a rectangle ⇒4a=2(1+b) ⇒2a=(1+b) ⇒a=(1+b)∕2⋅⋅⋅⋅⋅⋅⋅(i) They differ in area = 1 square cm ⇒a2−lb=1 ⇒[(1+b)∕2]2−lb=1 ⇒(l2+b2+2lb)∕4−lb=1 ⇒12+b2+2lb−4lb=4 ⇒12+b2−2lb=4 ⇒(1−b)2=4[∵(a−b)2=a2+b2−2ab] ⇒1−b=2