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Answer:
The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
Step-by-step explanation:
At first, let us find the perimeter of the playground
∵ Perimeter of a triangle is P = S1 + S2 + S3
∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft
∴ S1 = 2x, S2 = x - 1, S3 = x
→ Substitute them in the rule of the perimeter above
∵ P = 2x + x - 1 + x
→ Add the like terms
∴ P = (2x + x + x) - 1
∴ P = 4x - 1
∵ The perimeter of this playground is 27 feet
∴ P = 27
→ Equate the two values of P
∴ 4x - 1 = 27
→ Add 1 to both sides
∴ 4x - 1 + 1 = 27 + 1
∴ 4x = 28
→ Divide both sides by 4
∵ =
∴ x = 7
→ Substitute the value of x in each side to find their lengths
∵ S1 = 2(7)
∴ S1 = 14 feet
∵ S2 = 7 - 1
∴ S2 = 6 feet
∵ S3 = 7 feet
∴ The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet