The sides of the triangle occur in a ratio of 4 : 7 : 2, so if <em>x</em> is some positive number, then we can write each side's length in terms of <em>x</em> as 4<em>x</em>, 7<em>x</em>, and 2<em>x</em>.
The perimeter is 299 yd, so
4<em>x</em> + 7<em>x</em> + 2<em>x</em> = 299 yd
13<em>x</em> = 299 yd
<em>x</em> = (299 yd) / 13
<em>x</em> = 23 yd
Then the sides of the triangle have lengths of
4<em>x</em> = 4 • 23 yd = 104 yd
7<em>x</em> = 7 • 23 yd = 161 yd
2<em>x</em> = 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.
