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A triangle has side lengths of (9.3 p-1.3 q) centimeters, (9.6 p+6.9 r) centimeters, and (4.2 r+3.1 q) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 7.3 r+18.9 p+5.6 q 8pq+16.5 pr+7.3 qr 8.7 qr+23.1 pr 18.9 p+1.8 q+11.1 r

A triangle has side lengths of (9.3p−1.3q) (9.3 p-1.3 q) centimeters, (9.6p+6.9r) (9.6 p+6.9 r) centimeters, and (4.2r+3.1q) (4.2 r+3.1 q) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline7.3r+18.9p+5.6q 7.3 r+18.9 p+5.6 q \newline8pq+16.5pr+7.3qr 8 p q+16.5 p r+7.3 q r \newline8.7qr+23.1pr 8.7 q r+23.1 p r \newline18.9p+1.8q+11.1r 18.9 p+1.8 q+11.1 r

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Q. A triangle has side lengths of (9.3p−1.3q) (9.3 p-1.3 q) centimeters, (9.6p+6.9r) (9.6 p+6.9 r) centimeters, and (4.2r+3.1q) (4.2 r+3.1 q) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?\newline7.3r+18.9p+5.6q 7.3 r+18.9 p+5.6 q \newline8pq+16.5pr+7.3qr 8 p q+16.5 p r+7.3 q r \newline8.7qr+23.1pr 8.7 q r+23.1 p r \newline18.9p+1.8q+11.1r 18.9 p+1.8 q+11.1 r
  1. Add Side Lengths: To find the perimeter of the triangle, we need to add the lengths of all three sides together. The side lengths are given as (9.3p−1.3q)(9.3p - 1.3q) cm, (9.6p+6.9r)(9.6p + 6.9r) cm, and (4.2r+3.1q)(4.2r + 3.1q) cm. Let's add these expressions together to get the perimeter.\newlinePerimeter = (9.3p−1.3q)+(9.6p+6.9r)+(4.2r+3.1q)(9.3p - 1.3q) + (9.6p + 6.9r) + (4.2r + 3.1q)
  2. Combine Like Terms: Now, we combine like terms to simplify the expression. We will add the coefficients of pp, qq, and rr separately.\newlinePerimeter = (9.3p+9.6p)+(−1.3q+3.1q)+(6.9r+4.2r)(9.3p + 9.6p) + (-1.3q + 3.1q) + (6.9r + 4.2r)
  3. Perform Addition: Perform the addition for each variable.\newlinePerimeter = 18.9p+1.8q+11.1r18.9p + 1.8q + 11.1r
  4. Final Perimeter: The simplified expression for the perimeter is 18.9p+1.8q+11.1r18.9p + 1.8q + 11.1r centimeters. This matches one of the given options.

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