Answer:
Width is 20 inches.
Length is 44 inches.
Step-by-step explanation:
Recall that the perimeter of a rectangle is given by the formula:
[tex]P=2(l+w)[/tex]
Where l is the length and w is the width.
We know that the length is 4 more than double the width. In other words, we can write an equation for l:
[tex]l=4+2w[/tex]
Let's substitute this into the above equation. So:
[tex]P=2((4+2w)+w)[/tex]
Combine like terms:
[tex]P=2(4+3w)[/tex]
We are given that the perimeter is 128 (inches). So, substitute 128 for P and solve for w:
[tex]128=2(4+3w)[/tex]
Divide both sides by 2. The right side cancels:
[tex]64=4+3w[/tex]
Subtract 4 from both sides:
[tex]3w=60[/tex]
Divide both sides by 3:
[tex]w=20[/tex]
Therefore, our width is 20.
We can use the length formula we acquired previously to acquire length. We have:
[tex]l=4+2w[/tex]
Substitute 20 for w:
[tex]l=4+2(20)[/tex]
Multiply:
[tex]l=4+40[/tex]
Add:
[tex]l=44[/tex]
So, our length is 44.
And we width is 20.
And we're done!
