Question

What is the length of a side of the pentagon?

Answer 1

The length of a side of a pentagon is 69 units.

Since the hexagon on the left has 6 sides, and all of the sides have an equal length, if you multiply the number of sides(6) by the length of one side (3x+5) you will get the perimeter of the hexagon, 6(3x+5)
This is the same for the pentagon as well, since the pentagon on the right has 5 sides, and all of the sides have an equal length, if you multiply the number of sides(5) by the length of one side (4x-1) you will get the perimeter of the pentagon, 5(4x-1)

Now we have the equation for the perimeter of the hexagon, 6(3x+5), and the pentagon 5(4x-1). Since we know that the perimeters are the same length for each shape, we can set these two formulas equal to each other

Here is how I set up my equation
6(3x+5)=5(4x-1)

Now that you have the equation, you must solve for x, which I will demonstrate the steps down below

6(3x+5)=5(4x-1)
18x+30=20x-5 (subtract 18x on both sides)
30=2x-5 (subtract -5 on both sides)
35=2x (divide 2 on each side)
17.5=x

Now that you have determined that x is 17.5, all that is left to do is plug in 17.5 into the equation that solves for one side of the pentagon(4x-1) to get the length of a side of a pentagon, which is your answer.

Here is the work if needed
4(17.5)-1
70-1
69

The length of a side of a pentagon is 69 units.

I hope this helped!
Leave a comment on my answer if you have any questions on what I said here or need any more help with math.