9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2 (x+6) feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?

Question

Jaydin Roman

Mathematics

16 August, 17:12

9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2 (x+6) feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?

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Answers (1)

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Erin · Answer 1

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