Question

you decide to put a 3 foot wide path around the 484 square yards garden. what is the perimeter of the outside path of the garden? your answer thinking about the previous problem, how much is each side of the square? explain your solution. your answer

Explanation:

Step1: Find side length of square garden

Let the side length of the square garden be $s$. Given the area $A = 484$ square yards. Since $A=s^{2}$, then $s=\sqrt{484}=22$ yards.

Step2: Adjust side length for path

The path is 3 feet wide. Since 3 feet = 1 yard, the side length of the outer - square (including the path) is $s_{outer}=22 + 2\times1=24$ yards.

Step3: Calculate perimeter of outer path

The perimeter $P$ of a square is $P = 4s$. For the outer - square, $P=4\times24 = 96$ yards for the outer - square of the garden with the path. But we need to consider the path itself. The path adds an extra length on each side. Each side of the path has an extra length of 2 yards (1 yard on each end). So the total extra length for the 4 sides is $4\times4 = 16$ yards. The perimeter of the outside path is $96+40=136$ yards. The side length of the original square garden is 22 yards as calculated from the area formula $A = s^{2}$ where $s=\sqrt{484}=22$ yards.

Answer:

First sub - question:

136 yards

Second sub - question:

22 yards