The sides of the triangle occur in a ratio of 4 : 7 : 2, so if x is some positive number, then we can write each side's length in terms of x as 4x, 7x, and 2x.
The perimeter is 299 yd, so
4x + 7x + 2x = 299 yd
13x = 299 yd
x = (299 yd) / 13
x = 23 yd
Then the sides of the triangle have lengths of
4x = 4 • 23 yd = 104 yd
7x = 7 • 23 yd = 161 yd
2x = 2 • 23 yd = 46 yd
"Median" here refers to the side length between the shortest and longest sides, so the answer would be 104 yd.