A rectangular garden, with length twice its width, is to be expanded so that both sides are increased by 3 m.
a.) How would you represent the width of the original garden?
b.) How would you represent the width of the new garden? How about the length?
c.) Suppose the width of the original garden is 2 m, what would be the area of the new garden?
a) let the width be a letter i.e. any letter of the alphabet, it doesn't matter although preferably w.
b) w+3 for the new width, 2w+3 for the new length
c) new width is 2+3
new length is 4+3, multiply together for the new area
a.) To represent the width of the original garden, we can assign a variable. Let's say we represent the width as 'w', where 'w' is a positive number.
b.) To represent the width of the new garden, we need to add 3 meters to the original width. So the width of the new garden can be represented as 'w + 3'.
Since the length of the rectangular garden is twice its width, we can represent the length of the original garden as '2w'. For the new garden, we need to add 3 meters to both sides of the original garden, so the length can be represented as '2w + 3'.
c.) If the width of the original garden is 2 meters, we can substitute this value into the expressions for the width and length of the new garden derived in part b:
Width of the new garden = 2 + 3 = 5 meters
Length of the new garden = 2(2) + 3 = 7 meters
To find the area, multiply the width by the length:
Area = Width × Length = 5 × 7 = 35 square meters
Therefore, if the width of the original garden is 2 meters, the area of the new garden would be 35 square meters.