Question

The lengths of the sides of a 6 sided polygon are an arithmetic sequence. The length of the shortest side is 3 meters. If the length of the next longer side is 5 meters, what is the length of the longest side?

Answer 1

Length of the longest side = 13 meters

Explanation:

Given:

The sides of six sided polygon are in arithmetic sequence.

Length of the shortest side = 3 meters

Length of next longer side = 5 meters

To find the length of the longest side.

Solution:

The sides of the polygon are in arithmetic sequence. Thus, the sides can be given as:

`a,(a+d),(a+2d),(a+3d),(a+4d),(a+5d)`

where
`a` is the shortest side and
`d` is common difference between the sides.

We are given the lengths of the shortest side and the next longer side.

Thus we have:

`a=3\ m`

`a+d=5\ m`

Using substitution, we can find the value of
`d`

Plugging in
`a=3` in
`a+d=5`,

`3+d=5`

Subtracting both sides by 3.

`3-3+d=5-3`

∴
`d=2`

From the sequence, we see that the length of the longest side is =
`a+5d`

Plugging in the know values of
`a` and
`d`.

Length of the longest side =
`3+5(2)=3+10=13\ m`