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
)
.
Part A:
P = 2(l + w)
Distribute the 2:
P = 2l + 2w
Subtract 2l from both sides:
P - 2l = 2w
Divide both sides by 2:
(w)
P - 2l = —
2
w
(w = P/2 - l)
Therefore, the formula for the perimeter of a rectangle in terms of the width w is:
w = P/2 - l
Part B:
In order to isolate the variable w in the equation P = 2(l + w), I followed the steps of algebraic manipulation. I first distributed the 2 and then simplified the equation by subtracting 2l from both sides. This left me with 2w on one side of the equation. Finally, I divided both sides by 2, resulting in w = P/2 - l. This process allowed me to isolate the variable w and solve for it in terms of the other variables in the equation.