Answer:
[tex] length = 12 ft [/tex]
[tex] width = 8 ft [/tex]
Step-by-step explanation:
Earl's garden:
[tex] length = (x + 6) ft [/tex]
[tex] width = (x + 2) ft [/tex]
[tex] perimeter = 2(length) + 2(width) [/tex]
[tex] perimeter = 2(x + 6) + 2(x + 2) [/tex]
[tex] perimeter = 2x + 12 + 2x + 4 = (4x + 16) ft [/tex]
Dylan's garden:
[tex] length = (2x - 2) ft [/tex]
[tex] width = (x + 4) ft [/tex]
[tex] perimeter = 2(length) + 2(width) [/tex]
[tex] perimeter = 2(2x - 2) + 2(x + 4) [/tex]
[tex] perimeter = 4x - 4 + 2x + 8 = (6x + 4) ft [/tex]
Generate an equation to solve for the value of x.
Since the perimeters of both gardens are the same, therefore:
[tex] 6x + 4 = 4x + 16 [/tex]
Collect like terms
[tex] 6x - 4x = - 4 + 16 [/tex]
[tex] 2x = 12 [/tex]
Divide both sides by 2
[tex] x = 6 [/tex]
Earl's garden:
[tex] length = (x + 6) ft [/tex]
Plug in the value of x
[tex] length = 6 + 6 = 12 ft [/tex]
[tex] width = (x + 2) ft = 6 + 2 = 8 ft [/tex]
