Answer:
367 yards
Step-by-step explanation:
If we let x and y represent the length and width, respectively, then the problem statement can be translated to ...
x = 10y -13
xy = 13946
Substituting the first equation into the second gives ...
(10y -13)y = 13946
10y^2 -13y -13946 = 0 . . . . rearranged to standard form
Using the quadratic formula
x = (-b±√(b^2-4ac))/(2a) . . . gives the solutions to ax^2 +bx +c = 0
we can find the positive value of y to be
y = (-(-13) +√((-13)^2 -4(10)(-13946)))/(2·10) = (13 +√558009)/20
y = 38
The corresponding value of x is ...
x = 10·38 -13 = 367
The length of the rectangle is 367 yards.
