perimeter of the recangle

Question

A farmer has 70 meters of fencing and would ike to use the fencing to create a rectangulax garden in the middlc of an open feld

Let I represent the varying length of the rectangular garden (in meters).

a. Suppose the length of the garden is 25 meters (l=25).

 i. What is the width of the garden? meters

  ii What is the area of the garden? square meters 

b. Write an expression in terms of I that represents the width of the garden (in meters) 

c. Write an expression in terms of I that represents the area of the garden (in meters)

Answer 1

Given Perimeter of the Garden (P) = 70m

Let Length of the Garden = L

Width of the Garden = W

Given that the Garden is in Rectangular Shape

Perimeter of the Rectangle ( P ) = 2 ( L + W )  ----------------->  (1)

Area of the Rectangle (A) = L X B  -------------------------->  (2)

a)

i)

L = 25m

Substitute L = 25 and P = 70 in Eq (1)

70  =  2( 25 + W )

25 + W  =  70  / 2

25 + W  =  35

W  =  35 - 25

W  = 10m.

ii)

Substitute L = 25 and W = 10 in Eq (2)

A  =  25 X 10

A  =  250 m^2

b)

Substitute L = l and P = 70 in Eq (1)

70  =  2 ( l + W )

l + W  =  70 / 2

l + W  =  35

W  =  35 - l.

c)

Substitute L = l and W = 35 - l in Eq (2)

A  =  l X (35 - l)

A  =  35l - l^2

Answer :

a)

i)  W  = 10m.

ii)  A  =  250 m^2

b)  W  =  35 - l.

c)  A  =  35l - l^2