Answer:
1) Known information:
- The perimeter.
- [tex]width=lenght-3ft[/tex]
- The formula of the perimeter of the rectangle:
[tex]P=2l+2w[/tex]
Unknown information:
- The value of the widht.
- The value of the length.
2) Equation:
[tex]530=2l+2w\\530=2l+2(l-3)[/tex]
3) [tex]l=134\\w=131[/tex]
Step-by-step explanation:
1. The problem gives you the perimeter, the formula of the perimeter of a rectangle and says that the width of a rectangle is 3 feet shorter than its length ([tex]w=l-3[/tex]), but does not give the value of the widht and the value of the lenght.
2. Based on the information given, you can write the following equation:
[tex]530=2l+2w[/tex]
Where [tex]l[/tex] is the lenght and [tex]w[/tex] is the width.
Substitute [tex]w=l-3[/tex] into the equation above, then you have:
[tex]530=2l+2(l-3)[/tex]
3. Solve for the lenght:
[tex]530=2l+2(l-3)\\530=2l+2l-6\\536=4l\\l=134[/tex]
4. Know you can calculate the width:
[tex]w=l-3=134-3=131[/tex]
5. Therefore, the length is 134 feet and the widht is 131 feet.
