Let the length be [tex]l[/tex] in this equation.
We know that the perimeter of a rectangle is [tex]w2 + l2 = P[/tex]
Width is defined in terms of length, so we know [tex]w = l2 - 20[/tex]
We can substitute this value of w into the formula for perimeter to find the length.
[tex](l2 - 20)2 + l2 = 182[/tex]
[tex]l4 - 40 + l2 = 182[/tex]
[tex]l4 + l2 = 222[/tex]
[tex]l6 = 222[/tex]
[tex]l = 37[/tex]
So the length is 37. Now that we've found the length, we can go back to the Perimeter formula again and find width.
[tex]w2 + (37)2 = 182[/tex]
[tex]w2 + 74 = 182[/tex]
[tex]w2 = 108[/tex]
[tex]w = 54[/tex]
Width is 54. Now with both of these values found, we can calculate area with the formula [tex]l * w = A[/tex]
[tex]37 * 54 = A[/tex]
[tex]1998 = A[/tex]
So the area of the rectangle is 1998 yards^2.
