Sumali sa IDNStudy.com para sa detalyadong mga sagot sa iyong mga tanong. Makakuha ng hakbang-hakbang na mga gabay para sa lahat ng iyong teknikal na tanong mula sa mga miyembro ng aming komunidad.
Sagot :
The name of a regular polygon can be name as n-gon where where n is the number of sides of a polygon.
In order to find the name of a regular polygon, we have to get the number of sides of a polygon with the given number of diagonals by using the formula
no. of diagonals = n(n-3) / 2 where n is the no. of sides
90 = n(n-3) / 2
90 = (n^2 - 3n) / 2
90×2 = n^2 - 3n
180 = n^2 - 3n
0 = n^2 - 3n - 180
0 = (n - 15)(n + 12)
n - 15 = 0 n + 12 = 0
n = 15 n = -12
We have two values of n which are 15 and -12. But we will not consider n = -12 because there is no possibility to have a negative number of sides of a polygon.
So we have 15 number of sides of a polygon.
Therefore the name of a regular polygon that has 90 diagonals is 15-gon or pendedecagon.
In order to find the name of a regular polygon, we have to get the number of sides of a polygon with the given number of diagonals by using the formula
no. of diagonals = n(n-3) / 2 where n is the no. of sides
90 = n(n-3) / 2
90 = (n^2 - 3n) / 2
90×2 = n^2 - 3n
180 = n^2 - 3n
0 = n^2 - 3n - 180
0 = (n - 15)(n + 12)
n - 15 = 0 n + 12 = 0
n = 15 n = -12
We have two values of n which are 15 and -12. But we will not consider n = -12 because there is no possibility to have a negative number of sides of a polygon.
So we have 15 number of sides of a polygon.
Therefore the name of a regular polygon that has 90 diagonals is 15-gon or pendedecagon.
There is a formula for finding the number of sides of a polygon given diagonals, which is:
D=[tex]\frac{n(n-3)}{2}[/tex]
where:
D=diagonals
n=number of sides
Now substitute:
90=[tex]\frac{n(n-3)}{2}[/tex]
Multiply both sides with 2
180=n(n-3)
Distribute n
180=n²-3n
Equate it to Ax²+By+C=0
n²-3n-180=0
Factor:
(n-15)(n+12)=0
n-15=0 n+12=0
n=15 n=-12
Since there are no negative sides, then we consider n=15
the name of the polygon that has 90 diagonals is pentadecagon
Hope this helps =)
D=[tex]\frac{n(n-3)}{2}[/tex]
where:
D=diagonals
n=number of sides
Now substitute:
90=[tex]\frac{n(n-3)}{2}[/tex]
Multiply both sides with 2
180=n(n-3)
Distribute n
180=n²-3n
Equate it to Ax²+By+C=0
n²-3n-180=0
Factor:
(n-15)(n+12)=0
n-15=0 n+12=0
n=15 n=-12
Since there are no negative sides, then we consider n=15
the name of the polygon that has 90 diagonals is pentadecagon
Hope this helps =)
Salamat sa iyong kontribusyon. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. Umaasa kami na natagpuan mo ang hinahanap mo sa IDNStudy.com. Bumalik ka para sa mas maraming solusyon!