Answer to Question #199701 in Calculus for Solomon Augustine

Question

Consider a rectangle with perimeter 28 (units). Let the width of the 

rectangle be w (units) and let the Area of the region enclossed by the 

rectangle be A ( square units). 

 Express A as a function of w and state the domain and range of the 

 function.

Answer 1

We know that the perimeter of rectangle can be given as,

$P = 2L+2W$

$L = \dfrac{P-2W}{2}$

$P = 28(units)$

Hence, $L = 14-W$

Now area $A$ can be calculated as,

$A = L \times W$

$A = (14-W)W$

$A = 14W-W^2$

Domain : $0<W<14$

Range : $0<A<49$