Question

If form a wire of length $36$ metre, a rectangle of greatest area is made, then find its two adjacent sides in metre.

• A. $9$ & $9$
• B. $8$ & $10$
• C. $6$ & $12$
• D. $3$ & $15$

Answer 1

The correct option is A $9$ & $9$

Let the length be $x$.
Hence the breadth of the rectangle will be $y$.
Therefore
$2(x+y)=36$ or $x+y=18$ or $y=18-x$.
Now area of the rectangle will be
$A=xy$
$=x(18-x)$
$=18x-x^2$.
Differentiating the are a with respect to $x$, we get
$18-2x=0$
$x=9$m.
Hence
$y=18-9=9m$.
Hence the length of the adjacent sides are $9m$ and $9m.$