Problem

A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 18 feet more than the length of the shortest side. Find the dimensions if the perimeter is 154 feet.

Answer

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Answer

Final Answer: The dimensions of the triangle are \(\boxed{34}\) feet, \(\boxed{68}\) feet, and \(\boxed{52}\) feet.

Steps

Step 1 :Let's denote the shortest side of the triangle as \(x\).

Step 2 :According to the problem, one side is twice the length of the shortest side, so it is \(2x\).

Step 3 :The third side is 18 feet more than the length of the shortest side, so it is \(x + 18\).

Step 4 :The perimeter of a triangle is the sum of the lengths of its sides, so we can write the equation as \(x + 2x + (x + 18) = 154\).

Step 5 :Solving this equation, we find that \(x = 34\).

Step 6 :So, the shortest side of the triangle is \(34\) feet.

Step 7 :The side that is twice the length of the shortest side is \(2x = 68\) feet.

Step 8 :The side that is 18 feet more than the length of the shortest side is \(x + 18 = 52\) feet.

Step 9 :Final Answer: The dimensions of the triangle are \(\boxed{34}\) feet, \(\boxed{68}\) feet, and \(\boxed{52}\) feet.

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