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A triangle has side lengths of (2.1 w-6.3) centimeters, (8.5 w+3.4) centimeters, and (8.7 x+9.5) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 18.2 x-4.2 w+11.9 10.6 w+8.7 x+6.6 18.2 x+7.7 w 18.2 x+10.6 w-2.9

A triangle has side lengths of (2.1w−6.3) (2.1 w-6.3) centimeters, (8.5w+3.4) (8.5 w+3.4) centimeters, and (8.7x+9.5) (8.7 x+9.5) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline18.2x−4.2w+11.9 18.2 x-4.2 w+11.9 \newline10.6w+8.7x+6.6 10.6 w+8.7 x+6.6 \newline18.2x+7.7w 18.2 x+7.7 w \newline18.2x+10.6w−2.9 18.2 x+10.6 w-2.9

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Q. A triangle has side lengths of (2.1w−6.3) (2.1 w-6.3) centimeters, (8.5w+3.4) (8.5 w+3.4) centimeters, and (8.7x+9.5) (8.7 x+9.5) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline18.2x−4.2w+11.9 18.2 x-4.2 w+11.9 \newline10.6w+8.7x+6.6 10.6 w+8.7 x+6.6 \newline18.2x+7.7w 18.2 x+7.7 w \newline18.2x+10.6w−2.9 18.2 x+10.6 w-2.9
  1. Calculate Perimeter Formula: To find the perimeter of the triangle, we need to add the lengths of all three sides together. The perimeter PP is given by the formula P=side1+side2+side3P = \text{side1} + \text{side2} + \text{side3}.
  2. Add Side Lengths: Now, let's add the side lengths together: 2.1w−6.32.1w - 6.3 + 8.5w+3.48.5w + 3.4 + 8.7x+9.58.7x + 9.5.
  3. Combine Like Terms: Combine like terms. For the terms with ' extit{w}', we have 2.1w+8.5w2.1w + 8.5w, which equals 10.6w10.6w. For the constant terms, we have −6.3+3.4+9.5-6.3 + 3.4 + 9.5, which equals 6.66.6. The term with ' extit{x}' remains unchanged as there are no other ' extit{x}' terms to combine with, so it stays as 8.7x8.7x.
  4. Final Perimeter Expression: The expression for the perimeter is therefore 10.6w+8.7x+6.610.6w + 8.7x + 6.6.

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