Length: 2(x + 6); Width: 3.5x
A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.
The perimeter is the sum of the measures of all 4 sides.
perimeter = length + length + width + width
perimeter = 2(x + 6) + 2(x + 6) + 3.5x + 3.5x
Use the distributive property on 2(x + 6).
perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x
Now let's group all terms with x first, then all the numbers.
perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12
Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.
perimeter = 11x + 24
11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.
Answer: 11x + 24
