The yard is 6 yd by 15 yd.
Let's say we're going to make the border x yards wide. We'll have four corners that are each x^2 square yards in area, for a total of 4x^2 square yards. We'll have two sides that are 6-2 = 4x^2 yards in area. We'll have two sides that are 15-2 = 13x^2 square yards in area. The total area will be:
4x^2 + 2(4x^2) + 2(13x^2)
4x^2 + 8x^2 + 26x^2
38x^2
We have 46 square yards, so:
38x^2 = 46
x^2 = 46/38
x = sqrt(46/38)
x = 1.10023920844, or about 1.1 yards
1.1 yards = 1 yard 0.3 feet = 1 yard 3.6 inches
The width can be 1 yard 3.6 inches.