Answer:
[tex]Length = 105.5\ m[/tex]
Step-by-step explanation:
Given
[tex]Perimeter = 348[/tex]
[tex]Length = 37 + Width[/tex]
Required
Find the width
[tex]Length = 37 + Width[/tex]
Make Width the subject
[tex]Width = Length - 37[/tex]
The perimeter of a rectangular field is
[tex]Perimeter = 2 * (Length + Width)[/tex]
Substitute Length - 37 for Width
[tex]Perimeter = 2 * (Length + Length - 37)[/tex]
[tex]Perimeter = 2 * (2Length - 37)[/tex]
Open Bracket
[tex]Perimeter = 4Length - 74[/tex]
Substitute 348 for Perimeter
[tex]348 = 4Length - 74[/tex]
Solve for Length
[tex]4Length = 348 + 74[/tex]
[tex]4Length = 422[/tex]
Divide through by 4
[tex]Length = 422/4[/tex]
[tex]Length = 105.5[/tex]
