Which of the following formulas correctly gives the perimeter of a parallelogram with side lengths $a$ and $b$?

• A. $2a+b$
• B. $2(a+b)$
• C. $4a$
• D. $ab$

Answer: (B)

Verified step by step guidance

1. Recall that a parallelogram has two pairs of equal sides. If the side lengths are given as \(a\) and \(b\), then there are two sides of length \(a\) and two sides of length \(b\).
2. The perimeter of any polygon is the sum of the lengths of all its sides. For a parallelogram, this means adding the lengths of all four sides together.
3. Express the perimeter \(P\) as the sum of the sides: \(P = a + b + a + b\).
4. Combine like terms to simplify the expression: \(P = 2a + 2b\).
5. Factor out the common factor 2 to write the perimeter formula in a compact form: \(P = 2(a + b)\).