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A triangle has side lengths of 
(2.3 r-8.2 s) centimeters, 
(7.6 r+2.8 t) centimeters, and 
(1.5 t-2.5 s) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

10.4 rt-st-5.9 rs

9.9 r-10.7 s+4.3 t

9.9 r-6.7 s+0.3 t

11.4 rt-7.9 st

A triangle has side lengths of (2.3r8.2s) (2.3 r-8.2 s) centimeters, (7.6r+2.8t) (7.6 r+2.8 t) centimeters, and (1.5t2.5s) (1.5 t-2.5 s) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline10.4rtst5.9rs 10.4 r t-s t-5.9 r s \newline9.9r10.7s+4.3t 9.9 r-10.7 s+4.3 t \newline9.9r6.7s+0.3t 9.9 r-6.7 s+0.3 t \newline11.4rt7.9st 11.4 r t-7.9 s t

Full solution

Q. A triangle has side lengths of (2.3r8.2s) (2.3 r-8.2 s) centimeters, (7.6r+2.8t) (7.6 r+2.8 t) centimeters, and (1.5t2.5s) (1.5 t-2.5 s) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline10.4rtst5.9rs 10.4 r t-s t-5.9 r s \newline9.9r10.7s+4.3t 9.9 r-10.7 s+4.3 t \newline9.9r6.7s+0.3t 9.9 r-6.7 s+0.3 t \newline11.4rt7.9st 11.4 r t-7.9 s t
  1. Calculate Perimeter: To find the perimeter of the triangle, we need to add the lengths of all three sides together. \newlinePerimeter = (2.3r8.2s)+(7.6r+2.8t)+(1.5t2.5s)(2.3r - 8.2s) + (7.6r + 2.8t) + (1.5t - 2.5s)
  2. Combine Like Terms: Combine like terms by adding the coefficients of rr, ss, and tt respectively.\newlinePerimeter = (2.3r+7.6r)+(8.2s2.5s)+(2.8t+1.5t)(2.3r + 7.6r) + (-8.2s - 2.5s) + (2.8t + 1.5t)\newlinePerimeter = 9.9r10.7s+4.3t9.9r - 10.7s + 4.3t
  3. Match with Answer Choices: Check the answer choices to see which one matches the calculated perimeter.\newlineThe correct expression that matches our calculation is 9.9r10.7s+4.3t9.9r - 10.7s + 4.3t.

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