Okay, let's solve this step-by-step. We are given a rectangle where we know the perimeter [tex]\(P\)[/tex] and the length [tex]\(l\)[/tex], and we need to find the width [tex]\(w\)[/tex].
The perimeter [tex]\(P\)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2l + 2w \][/tex]
Our goal is to rearrange this formula to solve for [tex]\(w\)[/tex]:
1. Start with the perimeter formula for a rectangle:
[tex]\[ P = 2l + 2w \][/tex]
2. Subtract [tex]\(2l\)[/tex] from both sides to isolate the term with [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 substitute the given values for the perimeter [tex]\(P\)[/tex] and the length [tex]\(l\)[/tex] into the formula to find the width [tex]\(w\)[/tex]:
4. Given:
[tex]\[ P = 70 \][/tex]
[tex]\[ l = 22 \][/tex]
5. Substitute these values into the formula:
[tex]\[ w = \frac{70 - 2(22)}{2} \][/tex]
6. Calculate the expression inside the parentheses first:
[tex]\[ w = \frac{70 - 44}{2} \][/tex]
7. Subtract 44 from 70:
[tex]\[ w = \frac{26}{2} \][/tex]
8. Finally, divide 26 by 2:
[tex]\[ w = 13 \][/tex]
So, the width [tex]\(w\)[/tex] when the perimeter is 70 and the length is 22 is 13.
