A convex polygon is a polygon whose interior angles are between 0degrees and 180degrees. The number of diagonals D in a convex polygon is given by the formula d=1/2n(n-3) . Determine the number of sides n in a convex polygon that has 35=1/2n(n-3)?

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1 Answer
Jim G.
Nov 7, 2017

#n=10#

Explanation:

#35=1/2n(n-3)#

#"multiply both sides by 2 to eliminate the fraction"#

#35xx2=cancel(2)xx1/cancel(2)n(n-3)#

#rArrn(n-3)=70#

#"express in standard form "ax^2+bx+c=0#

#"to factor consider the factors of the product a-c which"#
#"sum to + b"#

#rArrn^2-3n-70=0larrcolor(blue)"in standard form"#

#"the factors of - 70 which sum to - 3 are - 10 and + 7"#

#rArr(n-10)(n+7)=0#

#"equate each factor to zero and solve for n"#

#n+7=0rArrn=-7larrcolor(red)"not valid"#

#n-10=0rArrn=10#

#"since "n>0rArr" number of sides "=10#

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