Answer:
15 inches
Step-by-step explanation:
Okay, so we know a pentagon has 5 sides total. We also know that 3 of the sides are the same length, so let's assume those sides are n length.
n + n + n + _ + _ = 4ft 11in
The fourth side is an inch less than n.
n + n + n + (n - 1inch) + _ = 4ft 11in
The last side is 6inches more than n.
n + n + n + (n - 1inch) + 9n + 6inches) = 4ft 11in
Now that we have out equation, lets convert the 4ft 11in into just inches. 4ft = 4 x 12 inches (48 inches). Then add the 11inches and you get 59.
Now our equation is in terms of inches,
we can combine the 3 ns to 3n.
3n + (n-1) + (n +6) + 59
Then we combine all the ns and get 6n -1 +6 =59
Simplify to 6n +5 =59
then to 6n = 54
Then to n = 9.
Since we are looking for the longest side, you have to substitute n in for the side that would have the longest measure, n + 6.
9 + 6 = 15.
15 inches is your answer.
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however to find the last two roots we need to solve the square equation:
. Now we know the discriminator, using the discriminator we're able to find the roots of the equation: 
. The roots of the square equation are 
and 
.
and 
.