Question

If from a wire of length 36 m, a rectangle of greatest area is made, then its two adjacent sides (in metre) are 

(A) 6, 12 

(B) 9, 9 

(C) 10, 8 

(D) 13, 5

Answer 1

Answer is (B) 9, 9

Given that

2(a + b) = 36

a + b = 18

The area of the rectangle is

ab = a(18 - a)

Now,  A = 18a - a²

That is, dA/da = 18 − 2a

Substituting dA/da = 0, we get

18 - 2a = 0 ⇒ a = 9; b = 9