Jenny is building a rectangular garden around a tree in her yard. The southwest corner of the garden will be 2 feet south and 3 feet west of the tree. The north east corner of the garden will be 1 foot north and 4 feet east of the tree. If jenny paves a path around the garden that is uniformly 3 feet wide, then what is the area of the path?
A. 117 square feet
B. 96 square feet
C. 75 square feet
D. 60 square feet
Stuck, please help!
garden size
east west = 7
north south = 3
so garden area = 21
outside path dimensions
7+3*2 = 13
3+3*2 = 9
so big rectangle area = 9*13 = 117
so path area =117 - 21
So the answer is B?
LOL, yes
Haha thanks!
To find the area of the path, we need to first calculate the dimensions of the inner garden and the outer garden.
Let's start by finding the dimensions of the inner garden. The southwest corner of the inner garden is 2 feet south and 3 feet west of the tree, and the northeast corner is 1 foot north and 4 feet east of the tree.
The length of the inner garden is the distance from the southwest corner to the northeast corner in the east-west direction. So, the length = 4 feet (east) - 3 feet (west) = 1 foot.
Similarly, the width of the inner garden is the distance from the southwest corner to the northeast corner in the north-south direction. So, the width = 1 foot (north) - 2 feet (south) = -1 foot.
However, since we cannot have a negative width, we take the absolute value of -1 foot, so the width of the inner garden is 1 foot.
Now, we can calculate the area of the inner garden by multiplying the length by the width. So, the area of the inner garden = 1 foot x 1 foot = 1 square foot.
To find the dimensions of the outer garden, we need to add the width of the path on all sides to the dimensions of the inner garden. Since the path is uniformly 3 feet wide, we add 3 feet to each side of the dimensions.
The length of the outer garden = length of inner garden + (2 x width of path)
= 1 foot + (2 x 3 feet) = 1 foot + 6 feet = 7 feet.
The width of the outer garden = width of inner garden + (2 x width of path)
= 1 foot + (2 x 3 feet) = 1 foot + 6 feet = 7 feet.
Now, we can calculate the area of the outer garden by multiplying the length by the width. So, the area of the outer garden = 7 feet x 7 feet = 49 square feet.
Finally, to find the area of the path, we subtract the area of the inner garden from the area of the outer garden.
Area of the path = Area of the outer garden - Area of the inner garden
= 49 square feet - 1 square foot
= 48 square feet.
Therefore, the area of the path around the garden is 48 square feet.
None of the options provided match the correct answer, so the correct answer may be missing from the options.