Final answer:
To solve for the median side length of a triangle with sides in the ratio 2:7:6 and a perimeter of 345 yards, you find the value of x that satisfies the total perimeter and multiply it by 7 to get the median side, which is 161 yards.
Step-by-step explanation:
To find the measure of the median side of a triangle with side ratio 2:7:6 and a perimeter of 345 yards, you first need to recognize that the sides of the triangle can be represented as 2x, 7x, and 6x, where x is a common multiple. Since the perimeter is the sum of all sides, we can write the equation 2x + 7x + 6x = 345. Simplifying this, we get 15x = 345, and solving for x yields x = 23 yards.
Now, since we are looking for the median side, which is represented by 7x in the ratio, we multiply 7 by our found value of x to get the measurement of the median side. Therefore, 7 * 23 yards = 161 yards.