The perimeter of this hexagon is 162 cm. Each longer side measures 1 cm more than twice a shorter side. Find the length of the side labeled x.

Question

Here's what the hexagon looks like on my worksheet, just in case. http://imgur.com/5YxRcMf

 

And I still don't quite understand how to find the length of the side labeled x.

Answer 1

Hi Megan, in your sketch, you have four short sides and two long sides.

 

The perimeter of a polygon is the sum of the sides.

 

Let x represent the shorter sides, then 2x + 1 would represent the longer sides.

 

There are four short sides and two long sides. The perimeter is 162 cm.

 

The equation:

 

4x + 2(2x + 1) = 162

 

4x + 8x + 2 = 162

 

8x + 2 = 162

 

Subtract 2 from both sides.

 

8x = 160

 

Divide both sides by 8.

 

x = 20

 

The shorter sides are 20 cm in length. The longer sides are 2x + 1, or 41 cm in length.

 

Check:

 

4 * 20 + 2 * 41 = 162

 

80 + 82 = 162

 

162 = 162, values check.

 

Questions?