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Combine Like Terms (Basic, Integers)

A triangle has side lengths of [tex]\((8w + 8x)\)[/tex] centimeters, [tex]\((3w + 10y)\)[/tex] centimeters, and [tex]\((4y + 8x)\)[/tex] centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

A. [tex]\(13wy + 16wx + 12xy\)[/tex]
B. [tex]\(16x + 11w + 14y\)[/tex]
C. [tex]\(15wy + 26xy\)[/tex]
D. [tex]\(11w + 18x + 12y\)[/tex]

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Score: [tex]\(2 / 3\)[/tex]
Penalty: none

Sagot :

GinnyAnsweridn
To find the perimeter of a triangle with given side lengths, you need to add all three sides together and combine any like terms. The side lengths given are:

1. [tex]\(8w + 8x\)[/tex] centimeters
2. [tex]\(3w + 10y\)[/tex] centimeters
3. [tex]\(4y + 8x\)[/tex] centimeters

Let's add these expressions step-by-step:

### Step 1: Write the full addition of the side lengths.

[tex]\[ (8w + 8x) + (3w + 10y) + (4y + 8x) \][/tex]

### Step 2: Group the coefficients of each variable [tex]\(w\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex].

- For [tex]\(w\)[/tex]:
[tex]\[ 8w + 3w = 11w \][/tex]

- For [tex]\(x\)[/tex]:
[tex]\[ 8x + 8x = 16x \][/tex]

- For [tex]\(y\)[/tex]:
[tex]\[ 10y + 4y = 14y \][/tex]

### Step 3: Combine the grouped terms to form the perimeter expression.

Putting it all together, the expression for the perimeter of the triangle is:

[tex]\[ 11w + 16x + 14y \][/tex]

Therefore, the expression that represents the perimeter, in centimeters, of the triangle is:

[tex]\[ 11w + 16x + 14y \][/tex]
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