Question

The side length of a square is represented by the expression n - 1 Which are equivalent expressions for the perimeter of the square? Choose all that apply.

A n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5

B 2(n - 1.5) + 2(n - 1.5)

C 4n - 1.5

D 1.5n - 4

E 4(n - 1.5)

Answer 1

The correct expression for the perimeter of a square with side length (n - 1) is 4n - 4. None of the given options (A, B, C, D, E) are equivalent to this expression.

Step-by-step explanation:

The perimeter of a square is calculated by adding all four of its side lengths together. Since the side length is represented by n - 1, to find the perimeter, you would multiply this expression by 4, because there are four equal sides in a square. Hence, the equation for the perimeter (P) would be P = 4(n - 1), which simplifies to P = 4n - 4.

Therefore, the equivalent expressions for the perimeter of the square based on the given options would be those that simplify to 4n - 4. Let's evaluate the options given:

• A) n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5: This expression simplifies to 4n - 6, which is not equivalent to 4n - 4.
• B) 2(n - 1.5) + 2(n - 1.5): This simplifies to 4n - 6, which also is not equivalent to 4n - 4.
• C) 4n - 1.5: This is not correct because it is not equivalent to the perimeter expression 4n - 4.
• D) 1.5n - 4: This is incorrect as well, as the coefficient of n should be 4 for the perimeter, and the constant -4 is out of place.
• E) 4(n - 1.5): This option simplifies to 4n - 6, which is not correct either.

Thus, none of the given options is equivalent to the correct expression for the perimeter, 4n - 4.