Question

A rectangular field is to have an area of 100m2 and is to be surrounded by a fence. The cost C of the fence is 18 dollars per meter of length. Express the total cost of the fence in terms of the width of the field (use the variable 'w' for width).?

Answer 1

Answer:

$C(w) =\dfrac{3600}{w}+36w$                    

Step-by-step explanation:

Let l be the length of rectangular field and w be the width of rectangular field.

Area = 100 square meter

Area of rectangular field

=$=\text{Lenght}\times \text{Breadth}\\\Rightarrow l\times w = 100\\\\\Rightarrow l = \dfrac{100}{w}$

Cost of fencing =  18 dollars per meter

Perimeter of rectangle

$= 2\times \text{(Length + Width)}\\=2(l + w)$

Total cost =

$\text{Cost of fencing}\times \text{Perimeter of fileld}\\=18\times 2(l+w)\\\\=18\times 2(\dfrac{100}{w} + w)\\\\=36(\dfrac{100 + w^2}{w})\\\\\Rightarrow C(w) =\dfrac{3600}{w}+36w\\\\\text{where w is the width of the field}$

is the required cost function.