Answer:
The median side measures 92 yards
Step-by-step explanation:
Let's call x, y, and z the measures of the sides of the triangle.
The ratios between them are:
[tex]\displaystyle \frac{x}{y}=\frac{4}{7}[/tex]
[tex]\displaystyle \frac{x}{z}=\frac{4}{2}=2[/tex]
The first ratio gives the relation:
[tex]\displaystyle y=\frac{7x}{4}[/tex]
The second ratio can be solved for z:
[tex]\displaystyle z=\frac{x}{2}[/tex]
Since the perimeter is 299 yards:
[tex]x+y+z=299[/tex]
Substituting the above relations:
[tex]\displaystyle x+\frac{7x}{4}+\frac{x}{2}=299[/tex]
Multiplying by 4:
[tex]4x + 7x+2x=1196[/tex]
Joining like terms:
[tex]13x=1196[/tex]
Dividing by 13:
[tex]x=1196/13[/tex]
x=92
Now calculate y:
[tex]\displaystyle y=\frac{7\cdot 92}{4}[/tex]
y = 161
[tex]\displaystyle z=\frac{92}{2}[/tex]
z=46
The median side measures 92 yards
