From the question, the shape of the garden bed is a rectangle
And we are told that the sides of the bed use a total of 30 ft of cedar boards. This 30 ft represents the perimeter of the garden
We are also told that each side is longer than 1 foot, this means the width can not be less than 1 foot
And also, the length and width have a measurement in whole feet, this means the length and width can not be a fraction or decimal
Part A requires us to draw 3 different rectangles that can have a perimeter of 30ft, taking into consideration that each side is longer than 1 foot and the length and width have a measurement in whole feet.
Perimeter of a rectangle = 2( Length + width) = 2( L + W)
2(L + W) = 30
Divide both sides by 2
L + W = 30/2
L + W = 15
This means that we have to get 3 whole numbers that can add up to 15 to get a perimeter of 30
8 + 7 = 15 ( That is Length = 8ft, width = 7ft)
10 + 5 = 15(That is Length = 10 ft, width = 5 ft)
12 + 3 = 15(That is Length = 12ft. width = 3 ft)
Part B
Garden bed 1
Length = 8ft
Breadth = 7ft
Area = 8 x 7 = 56ft^2
Garden bed 2
Length = 10ft
Breadth = 5ft
Area = 10 x 5 = 50ft^2
Garden bed 3
Length = 12ft
Breadth = 3ft
Area = 12 x 3 = 36ft^2