Question

The sides of a rectangle are $(6-x)cmand(x-3)cm$. If its area is maximum then x=

• A. $4$
• B. $4.5$
• C. $4.8$
• D. $4.6$

Answer 1

The correct option is B $4.5$

Given,

sides of a rectangle,

$L=(6-x),W=(x-3)$

$A=LW$

$=(6-x)(x-3)$

$\therefore A=-x^2+9x-18$

$\frac{dA}{dx}=\frac{d}{dx}(-x^2+9x-18)$

$=-2x+9$

For maximum area, substitute, $\frac{dA}{dx}=0$

$\Rightarrow -2x+9=0$

$\therefore x=4.5$