Final answer:
To determine the dimensions of Jack's yard, we can write the equation 2l + 2w = 175, where l is the length and w is the width. By substituting the expression for w and solving the equation, we find that the length is 29 feet and the width is 52 feet.
Step-by-step explanation:
To write an equation to determine the dimensions of Jack's yard, we need to let l be the length and w be the width of the yard. We know that the perimeter of a rectangle is given by the formula P = 2l + 2w. In this case, the perimeter is 175 feet.
The problem states that the width is 6 feet less than twice the length, so we can write w = 2l - 6. Now we can substitute this expression for w into the formula for perimeter: 2l + 2(2l - 6) = 175.
Simplifying the equation gives us 6l - 12 = 175. Adding 12 to both sides and then dividing by 6 gives the solution l = 29. Finally, substituting this value into the expression for w gives w = 2(29) - 6 = 52.