Question

A line segment of length $10cm$ is divided into two parts and a rectangle is formed with these as adjacent sides, then the dimensions of the rectangle in order that its area is maximum is

• A. $4,6$
• B. $5,5$
• C. $2,8$
• D. $10,10$

Answer 1

The correct option is B $5,5$

Total Length of line segment $10cm$

Let the length of one part of line segemnt be $x$

The other will be $10-x$

The area of the Rectangle is $f\left(x\right)=x(10-x)$

The condition for maximum area is $f^{\prime }\left(x\right)=0$

$⟹f^{\prime }\left(x\right)=\frac{d}{dx}10x-x^2$

$⟹f^{\prime }\left(x\right)=10-2x$

According to the conition

$10-2x=0$

$2x=10$

$x=5$

So the other side alos equals $5$