Question

Express the given quantity in terms of the indicated variable.

The perimeter (in cm) of a rectangle that is 6 cm longer than it is wide; w = width of the rectangle (in cm).

Short answer

The perimeter of the rectangle is$4w+12$ centimeter.

Step-by-step solution

Step 1. Concept used.

Add all the sides to compute the perimeter.

Step 2. Plug the values in the formula.

Here, length$=w+6$

The perimeter of the rectangle is

$\begin{array}{l}P=2l+2w\\ =2\left(w+6\right)+2w\end{array}$

Step 3. Calculate the perimeter.

Multiply

$A=2\left(w+6\right)+2w$

Apply distributive law: $a\left(b+c\right)=ab+ac$

$\begin{array}{l}A=2w+2\cdot 6+2w\\ A=2w+12+2w\\ A=4w+12\end{array}$