Respuesta :
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:
[tex]a,(a+d),(a+2d),(a+3d),(a+4d),(a+5d)[/tex]
where [tex]a[/tex] is the shortest side and [tex]d[/tex] is common difference between the sides.
We are given the lengths of the shortest side and the next longer side.
Thus we have:
[tex]a=3\ m[/tex]
[tex]a+d=5\ m[/tex]
Using substitution, we can find the value of [tex]d[/tex]
Plugging in [tex]a=3[/tex] in [tex]a+d=5[/tex],
[tex]3+d=5[/tex]
Subtracting both sides by 3.
[tex]3-3+d=5-3[/tex]
∴ [tex]d=2[/tex]
From the sequence, we see that the length of the longest side is = [tex]a+5d[/tex]
Plugging in the know values of [tex]a[/tex] and [tex]d[/tex].
Length of the longest side = [tex]3+5(2)=3+10=13\ m[/tex]
