Question

a non-regular Pentagon has 3 sides that are the same length. the 4th side is 6 inches longer than the length shared by 3 of the sides, and the 5th side is 1 inch shorter than 2 times the length of the shared side length. the perimeter of the Pentagon is 4 feet and 11 inchs. what is the length of the longest side?​

Answer 1

15 inches

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.