Before we start, let’s change length to a different variable. We will call it “y”.
Thus x = 5’ and y = 10’
Based on information from original cornhole opening we know:
(x)*(y) = 50ft^2 also we know y = 2x since 10 feet is twice the amount of 5 feet. Therefore the relationship of x and y can be written as the following (in terms of x only):
(x)*(2x) = 50 or 2x^2 = 50. Check your work to see that solving for x = 5 and y = 10 which matches the given information.
Since the problem states uniform growth of the new opening we can set our equation equal to 84 and solve for new value of x
2x^2 = 84 which gives value of 6.48’ Also from before y = 2x thus new y = 12.96’. Checking would give total area of 83.98’ which is slightly lower due to rounding.
You could also state new value of x would be sqrt of (84/50) since that would be ratio of impact.
Either way the width would increase 1.48’ and length would increase by 2.96’.