Final answer:
To find the dimensions of the yard, we can set up equations based on the given information. By solving these equations, we can determine the length and width of the yard. The length of the yard is 136 feet and the width of the yard is 48 feet.
Step-by-step explanation:
To solve this problem, we can represent the dimensions of the yard as variables: let's say the length is 'L' and the width is 'W'.
We are given that six times the length of the yard equals seventeen times the width:
6L = 17W
We are also given that the perimeter of the yard is 368 feet:
2L + 2W = 368
To find the dimensions of the yard, we can solve this system of equations.
We can start by isolating 'L' in the first equation:
L = (17/6)W
Now substitute this expression for 'L' into the second equation:
2((17/6)W) + 2W = 368
Simplify the equation:
34/6W + 2W = 368
Combine like terms:
(34/6 + 12/6)W = 368
Simplify and solve for 'W':
(46/6)W = 368
W = 48
Now substitute the value of 'W' back into the expression for 'L':
L = (17/6)(48)
L = 136
Therefore, the length of the yard is 136 feet and the width of the yard is 48 feet.