The Guide for Add Math Project Work F4 : SHEEP PEN

Solution

a.) Using length and width
A = 1400

b.) Method 1 : Using Calculus (differentiation)

Method 2 : Graphical Method
From (b) : A =
Construct table x=40, 41, …, 49, A=
Plot graph area A versus Length x
Construct table x= 44.5, 44.6, …, 45.5, A=
Plot graph area A versus Length x

From both table and graph, area is maximum when x=45, so y =

Method 3 : Completing the Square

c.) (i) ………….
………….

(ii) Method 1 : Using Calculus (differentiation)

Method 2 : Graphical Method
From (c) A =
Construct table x = 25, 26, ……, 35, A =
Plot graph Area versus Length
Construct table x= 29.5, 29.6,….., 30.5., A=
Plot graph Area versus Length

From both table and graph, area maximum when x=
Thus, enclosed area is maximum when length = 22.5m, and width = 30m

Method 3 : Completing square method

d.) …………….
y =
so area A =

Method 1 : Using calculus (differentiation)

Method 2 : Graphical method
From (d) , A=
Construct table x= 20.0, 2.5, ….24.5, A=
Plot the graph area versus length
Construct table x= 22.1, 22.2, …. 23.0, A =
Plot the graph area versus length

From the both table and graph, total maximum area is 1012.5

Method 3 : completing square

Further investigation

1 Rectangular sheep pen
Length =
2 Rectangular sheep pens
Sum of length =
3 Rectangular sheep pens
Sum of length =

By induction , sum of length n rectangular sheep pens =

Total area, A=