To express the formula [tex]\( P = 2l + 2w \)[/tex] in terms of the width [tex]\( w \)[/tex], we need to isolate [tex]\( w \)[/tex] on one side of the equation. Let's break it down step-by-step:
1. Start with the original formula for the perimeter [tex]\( P \)[/tex]:
[tex]\[
P = 2l + 2w
\][/tex]
2. Subtract [tex]\( 2l \)[/tex] from both sides of the equation to isolate the term involving [tex]\( w \)[/tex]:
[tex]\[
P - 2l = 2w
\][/tex]
3. Divide both sides by 2 to solve for [tex]\( w \)[/tex]:
[tex]\[
w = \frac{P - 2l}{2}
\][/tex]
Now, we can use this formula to find the width when the perimeter [tex]\( P \)[/tex] is 70 and the length [tex]\( l \)[/tex] is 22.
1. Substitute [tex]\( P = 70 \)[/tex] and [tex]\( l = 22 \)[/tex] into the formula:
[tex]\[
w = \frac{70 - 2 \cdot 22}{2}
\][/tex]
2. Calculate the expression inside the parentheses:
[tex]\[
70 - 2 \cdot 22 = 70 - 44 = 26
\][/tex]
3. Divide by 2 to find [tex]\( w \)[/tex]:
[tex]\[
w = \frac{26}{2} = 13
\][/tex]
Therefore, the width [tex]\( w \)[/tex] is [tex]\( 13 \)[/tex].
