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A triangle has side lengths of
(7w+9) centimeters,
(5w+8) centimeters, and
(10 x+2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

12 w+19+10 x

12 x+29 w

13+16 w+12 x

12 w+17+12 x

A triangle has side lengths of $(7 w+9)$ centimeters, $(5 w+8)$ centimeters, and $(10 x+2)$ centimeters. Which expression represents the perimeter, in centimeters, of the triangle? $\newline$ $12 w+19+10 x$ $\newline$ $12 x+29 w$ $\newline$ $13+16 w+12 x$ $\newline$ $12 w+17+12 x$

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Area and perimeter: word problems

Full solution

Q. A triangle has side lengths of

(7 w+9)

centimeters,

(5 w+8)

centimeters, and

(10 x+2)

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

\newline

12 w+19+10 x

\newline

12 x+29 w

\newline

13+16 w+12 x

\newline

12 w+17+12 x

Add Side Lengths: To find the perimeter of the triangle, we need to add the lengths of all three sides together.
First Side: The first side is $7w+9$ centimeters.
Second Side: The second side is $5w+8$ centimeters.
Third Side: The third side is $(10x+2)$ centimeters.
Combine Expressions: Now, we add the expressions for the three sides to get the perimeter: $(7w+9) + (5w+8) + (10x+2)$ .
Combine Like Terms: Combine like terms: $7w + 5w$ + $9 + 8$ + $10x + 2$ .
Simplify Expression: This simplifies to: $12w + 17 + 10x$ .
Perimeter Calculation: The expression $12w + 17 + 10x$ represents the perimeter of the triangle in centimeters.

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