Set up the following equations:
[tex]L + W = 110[/tex]
[tex]L - W = 20[/tex]
110 represents the lengths of the length and width of the triangle, as you'll divide total perimeter of the rectangle, 220, by 2 to find the individual lengths. 20 is the difference between the length and width.
We'll use elimination for this system of equations, as there are opposite coefficients for W in both equations. Combine the two equations:
[tex]2L = 130[/tex]
Divide both sides by 2 to get L by itself:
[tex]L = 65[/tex]
The length of the rectangle is 65 feet.
Plug this value into the second equation:
[tex]65 - W = 20[/tex]
Add W to both sides:
[tex]65 = 20 + W[/tex]
Subtract 20 from both sides:
[tex]45 = W[/tex]
The width of the rectangle is 45 feet.
