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Answer:
w = 2.5
Step-by-step explanation:
Write these 2 equations to represent the problem:
[tex]l=w+5\\2w+2l=20[/tex]
where w is width and l is length. This can then be solved as a system of equatios. I'll solve by substitution, and as the [tex]l[/tex] is already solved for at the top:
[tex]2w+2l=20\\2w+2(w+5)=20\\2w+2w+10=20\\4w+10=20\\4w=10\\w=2.5[/tex]
If you just need the width, then you're already done there. I'll find the other variable too, and then check it to be sure it's correct.
[tex]l=w+5\\l=(2.5)+5\\l=7.5[/tex]
Now, confirm that with the second equation:
[tex]2w+2l=20\\2(2.5)+2(7.5)=20\\5+15=20\\20=20[/tex]
The perimeter of a rectangle is the sum of its side lengths.
The width of the rectangle is 2.5 units
Represent the length with l and the width with w.
So, we have:
[tex]P =2 \times (l + w)[/tex] --- the formula of perimeter
The perimeter is 20 units.
So, we have:
[tex]20 =2 \times (l + w)[/tex]
Divide both sides of the equation by 2
[tex]10 =l + w[/tex]
The length is said to be 5 more than its width.
So, we have:
[tex]l =5 + w[/tex]
Substitute 5 + w for l in [tex]10 =l + w[/tex]
[tex]10 = 5 + w + w[/tex]
[tex]10 = 5 + 2w[/tex]
Subtract 5 from both sides
[tex]5 = 2w[/tex]
Divide both sides by 2
[tex]2.5 = w[/tex]
Rewrite as:
[tex]w =2.5[/tex]
Hence, the width of the rectangle is 2.5 units
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