Answer:
Length of the longest side = 13 meters
Step-by-step 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)](https://tex.z-dn.net/?f=a%2C%28a%2Bd%29%2C%28a%2B2d%29%2C%28a%2B3d%29%2C%28a%2B4d%29%2C%28a%2B5d%29)
where
is the shortest side and
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](https://tex.z-dn.net/?f=a%3D3%5C%20m)
![a+d=5\ m](https://tex.z-dn.net/?f=a%2Bd%3D5%5C%20m)
<em>Using substitution, we can find the value of </em>![d](https://tex.z-dn.net/?f=d)
Plugging in
in
,
![3+d=5](https://tex.z-dn.net/?f=3%2Bd%3D5)
Subtracting both sides by 3.
![3-3+d=5-3](https://tex.z-dn.net/?f=3-3%2Bd%3D5-3)
∴ ![d=2](https://tex.z-dn.net/?f=d%3D2)
From the sequence, we see that the length of the longest side is = ![a+5d](https://tex.z-dn.net/?f=a%2B5d)
Plugging in the know values of
and
.
Length of the longest side = ![3+5(2)=3+10=13\ m](https://tex.z-dn.net/?f=3%2B5%282%29%3D3%2B10%3D13%5C%20m)