Question

The formula for the perimeter of a rectangle is P=2(l+w).

Part A. Rewrite the formula for the perimeter of a rectangle in terms of the width, w. In your final answer, include all of your work.

Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).

Answer 1

Part A — work and final formula:

Start with P = 2(l + w)

Method 1 (divide first):
1. Divide both sides by 2: P/2 = l + w
2. Subtract l from both sides: P/2 − l = w

So w = P/2 − l.

Method 2 (distribute first):
1. Distribute: P = 2l + 2w
2. Subtract 2l from both sides: P − 2l = 2w
3. Divide both sides by 2: w = (P − 2l)/2 = P/2 − l

Part B — description of the process:

I isolated w by undoing the operations around it using inverse operations, working from the outside inward. Because w was inside parentheses multiplied by 2 and then added to l, I first removed the multiplication by dividing both sides by 2, and then removed the addition by subtracting l from both sides, keeping the equation balanced at each step.