Answer:
[tex]VW = 33[/tex]
Step-by-step explanation:
See attachment for complete question
Given
[tex]VY = 4x - 1[/tex]
[tex]VW = 5x + 3[/tex]
[tex]Perimeter = 112[/tex]
Required
Determine the length of VW
Perimeter is calculated as:
[tex]Perimeter = 2 * (Width + Length)[/tex]
This gives:
[tex]Perimeter = 2 * (VW + VY)[/tex]
Substitute values for VW, VY and Perimeter
[tex]112 = 2 * (4x - 1 + 5x + 3)[/tex]
Collect Like Terms
[tex]112 = 2 * (4x + 5x -1 +3)[/tex]
[tex]112 = 2 * (9x +2)[/tex]
Divide through by 2
[tex]56 = 9x + 2[/tex]
Collect Like Terms
[tex]9x = 56 - 2[/tex]
[tex]9x = 54[/tex]
[tex]x = 54/9[/tex]
[tex]x = 6[/tex]
Substitute 6 for x in [tex]VW = 5x + 3[/tex]
[tex]VW = 5 * 6 + 3[/tex]
[tex]VW = 30 + 3[/tex]
[tex]VW = 33[/tex]
