Question

below is a diagram showing a regular hexagon and a regular Pentagon. Each shape has a lengths of two sides shown in the terms of x or y. Find which of the two shapes has the greatest perimeter. You must clearly show how you found your answer.

Answer 1

To solve this, we work out the perimeter of the hexagon, by finding x,  and we work out the perimeter of the pentagon by find y, and the compare them:

Perimeter of the Hexagon:
Since it is a regular hexagon, all the sides are the same: This means we can say that:

4x - 2 = x + 4       (Now lets solve this)
4x = x + 6             ( Add both sides by 2 to get 4x alone)
3x = 6                   (Subtract both sides by x, to collect the x values)
x = 2                     (Divide both sides by 3 to get what just x is)

Now we work out the length of one side by substituting the value for x in
x + 4 = 2 + 4
= 6 

Now that we know the length of one side, we can multiply that by 6 to get the perimeter, because a hexagon has six sides.

6 * 6 = 36

Perimeter of the Pentagon
Since it is a regular Pentagon, all the sides are the same, just like the hexagon. This means we can say that:

5y - 8 = 2y + 1         (Now we solve this like we did before)
5y = 2y + 9               ( Add both sides by 8 to get 5y alone)
3y = 9                       (Subtract both sides by 2y, to collect the y values)
y = 3                         (Divide both sides by 3 to get what just y is)

Now we work out the length of one side by substituting the value for x in
2y + 1 = (2 * 3) + 1
= 7

Now that we know the length of one side, we can multiply that by 5 to get the perimeter, because a pentagon has 5 sides.

5 * 7 = 35


Since the perimeter of the hexagon is 36, and the perimeter of the pentagon is 35, we can see that:

The hexagon has the larger perimeter.