Of all the rectangles each of which has a perimeter 40 m find which one had maximum area find the - Maths - Application of Derivatives

Question

Of all the rectangles each of which has a perimeter 40 m find which
one had maximum area find the area also

Ashwini Kumar · Accepted Answer

Let l and b be the length and breadth of rectangle and A is its area
perimeter=2l+b⇒40=2l+b⇒20=l+b⇒b=20-l     
1Now,A=lb⇒A=l20-l⇒A=20l-l2Differentiating both sides w
r t
 l, we getdAdl=20-2lFor the maximum area, its derivative will be zero
∴dAdl=0⇒20-2l=0⇒2l=20⇒l=10 mPutting l=10 m in 1, we getb=20-10=10 m∴When length and breadth both are equal to 10 m, area will be maximum
Area=lb=10×10=100 m2

Of all the rectangles each of which has a perimeter 40 m find which one had maximum area.find the area also.