NDA2020MathematicsApplication of DerivativesActual
Let l be the length and b be the breadth of a rectangle such that l+b=k . What is the maximum area of the rectangle?
Options
- A2 k^2
- Bk^2
- Ck^2 2
- Dk^2 4
Correct answer
D. k^2 4
Step-by-step solution
l+b=K , where l= length, b= breadth. Area of the rectangle A=l b . A=l(K-l)=l K-l^2 For maximum area, d A d l =0 aligned & d d l (l k-l^2 )=0 & K-2 l=0 l= K 2 aligned Now, K 2 +b=K b=K- K 2 = K 2 Area, A=l b= K 2 K 2 = K^2 4