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A triangle has side lengths of
(4c+10 d) centimeters,
(c-5f) centimeters, and
(2f+9d) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

19 d-3f+5c

14 df+7cf

4f+12 d+5c

11 df+14 cd-4cf

A triangle has side lengths of $(4 c+10 d)$ centimeters, $(c-5 f)$ centimeters, and $(2 f+9 d)$ centimeters. Which expression represents the perimeter, in centimeters, of the triangle? $\newline$ $19 d-3 f+5 c$ $\newline$ $14 d f+7 c f$ $\newline$ $4 f+12 d+5 c$ $\newline$ $11 d f+14 c d-4 c f$

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Area and perimeter: word problems

Full solution

Q. A triangle has side lengths of

(4 c+10 d)

centimeters,

(c-5 f)

centimeters, and

(2 f+9 d)

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

\newline

19 d-3 f+5 c

\newline

14 d f+7 c f

\newline

4 f+12 d+5 c

\newline

11 d f+14 c d-4 c f

Identify Perimeter Calculation: The perimeter of a triangle is the sum of the lengths of its sides. To find the perimeter, we need to add the expressions for each side length together.
Add Side Length Expressions: Add the expressions for the side lengths: $(4c+10d) + (c-5f) + (2f+9d)$ .
Combine Like Terms: Combine like terms: $4c + c$ + $10d + 9d$ + $-5f + 2f$ .
Perform Addition: Perform the addition: $5c + 19d - 3f$ .
Final Perimeter Expression: The expression $5c + 19d - 3f$ represents the perimeter of the triangle in centimeters.

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