Answer:
The third side is
B. [tex]2x[/tex]
Step-by-step explanation:
Given:
Perimeter of triangle = [tex]10x+12y[/tex]
Two sides of the triangle are :
1) [tex]4x+14y[/tex]
2) [tex]4x-2y[/tex]
To find the third side.
Solution:
Let the third side be = [tex]z[/tex]
The perimeter can be given as sum of all 3 sides :
[tex]4x+14y+4x-2y+z[/tex]
Combining like terms.
[tex]4x+4x+14y-2y+z[/tex]
[tex]8x+12y+z[/tex]
The perimeter given = [tex]10x+12y[/tex]
So, we have:
[tex]8x+12y+z=10x+12y[/tex]
Solving for [tex]z[/tex]
Subtracting both sides by [tex]8x[/tex]
[tex]8x-8x+12y+z=10x-8x+12y[/tex]
[tex]12y+z=2x+12y[/tex]
Subtracting both sides by [tex]12y[/tex]
[tex]12y-12y+z=2x+12y-12y[/tex]
∴ [tex]z=2x[/tex]
Thus, the third side is = [tex]2x[/tex]
