Question

A rectangle has a width of 6 units and a perimeter of 32 units. What is the length of the rectangle?

• A. 8
• B. 10
• C. 12
• D. 14
• E. 16

Hint:

For perimeter problems, remember that the formula \( P = 2(L + W) \) relates the perimeter to the length and width of a rectangle. Isolate the unknown variable to solve for it.

Answer 1

The Correct Option is B

The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (\text{Length} + \text{Width}). \] We are told that the perimeter is 32 units, and the width is 6 units. Let the length be denoted by \( L \). Substituting the known values into the perimeter formula: \[ 32 = 2 \times (L + 6). \] Now, to simplify the equation, divide both sides by 2: \[ \frac{32}{2} = \frac{2 \times (L + 6)}{2}
\Rightarrow
16 = L + 6. \] Next, subtract 6 from both sides to solve for \( L \): \[ 16 - 6 = L
\Rightarrow
L = 10. \] Thus, the length of the rectangle is \( \boxed{10} \) units.