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The perimeter of a triangle is 56 inches. The second side is 2 inches more than twice the first side, and the third side is 18 inches less than three times the first side. Find the lengths of the three sides.

A) 10 inches, 22 inches, 24 inches
B) 12 inches, 26 inches, 20 inches
C) 14 inches, 28 inches, 22 inches
D) 16 inches, 30 inches, 18 inches

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Answer:

The correct answer is option D) 12 inches, 26 inches, 18 inches.

Step-by-step explanation:

To solve this problem, let's denote the lengths of the sides of the triangle as follows:

  • Let x represent the length of the first side.
  • The second side is 2 inches more than twice the first side, so its length is 2x+2.
  • The third side is 18 inches less than three times the first side, so its length is 3x−18.

According to the perimeter formula for a triangle, the sum of the lengths of its three sides is equal to the perimeter, which is 56 inches.

So, we can write the equation:

                x+(2x+2)+(3x−18)=56

Now, let's solve for x:

           x+2x+2+3x−18=56

           6x−16=56

           6x=56+16

           6x=72

           x=72/6

           x=12

Now, we have found the length of the first side: x=12 inches.

To find the lengths of the other two sides, we substitute x=12 into the expressions we derived earlier:

  • Length of the second side: 2x+2 = 2(12)+2 = 26 inches.
  • Length of the third side: 3x−18 = 3(12)−18 = 36−18 = 18 inches.

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