Answer
126 yards by 44 yards.
Work Step by Step
Step 1. Assume the width is $x$ yards; then the length would be $3x-6$ yards.
Step 2. The perimeter is given by $2(x+3x-6)=340$; we have $4x-6=170$ and $x=44$ yards, and $3x-6=3(44)-6=126$ yards.
Step 3. The dimensions are 126 yards by 44 yards.