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A triangle has side lengths of
(3.4 c-5.4) centimeters,
(7.2 c+2.8) centimeters, and
(9.4 d+8.6) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

9.4 d+6+10.6 c

10+18 d-2c

8c+18 d

-2.6+10.6 c+18 d

A triangle has side lengths of $(3.4 c-5.4)$ centimeters, $(7.2 c+2.8)$ centimeters, and $(9.4 d+8.6)$ centimeters. Which expression represents the perimeter, in centimeters, of the triangle? $\newline$ $9.4 d+6+10.6 c$ $\newline$ $10+18 d-2 c$ $\newline$ $8 c+18 d$ $\newline$ $-2.6+10.6 c+18 d$

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Area and perimeter: word problems

Full solution

Q. A triangle has side lengths of

(3.4 c-5.4)

centimeters,

(7.2 c+2.8)

centimeters, and

(9.4 d+8.6)

centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

\newline

9.4 d+6+10.6 c

\newline

10+18 d-2 c

\newline

8 c+18 d

\newline

-2.6+10.6 c+18 d

Perimeter Definition: The perimeter of a triangle is the sum of the lengths of its three sides.
Add Expressions: Add the expressions for the side lengths to find the perimeter: $\newline$ Perimeter = $(3.4c - 5.4) + (7.2c + 2.8) + (9.4d + 8.6)$
Combine Like Terms: Combine like terms for the variables $c$ and $d$ : $\text{Perimeter} = (3.4c + 7.2c) + (9.4d) + (-5.4 + 2.8 + 8.6)$
Calculate Coefficients: Calculate the coefficients for $c$ and the constants: $\text{Perimeter} = 10.6c + 9.4d + 6$
Final Perimeter Expression: The expression $10.6c + 9.4d + 6$ represents the perimeter of the triangle in centimeters.

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