Question

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 northeast 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

Answer 1

My best answer is B) 96 square feet

Using the tree as an origin point we know the location of both corners of the rectangular garden around the tree. this can help us find the area of perimeter of this rectangle -

the rectangle is 3 feet wide and 7 feet long - However only the numbers matter here because we will use them to find the values of the path Jenny is paving which can be depicted as a 3 ft wide border along the rectangular garden.

The values are 7 + 3+ 3 = 13 (I added 3 ft to each side )

and 3 + 3 + 3 = 9 ( added 3 ft border to each side)

Now we can find the area of this new larger rectangle

13 x 9 = 117

then we subtract the area of the garden within this larger rectangle so that we may be left with only the area of the path on the outside

7( Length of inside rectangle)  x 3 ( Width of inside rectangle) = 21 ft squared (area of inside garden)

so then the total area 117 - 21 ( internal area used for gardening)

Which gives us the final answer of B) 96 square feet