A serieous problem
Algebra
Level
1
A polygon has 16 sides. The lengths of the sides of the polygon, starting with the shortest side, form an arithmetic sequence with common difference d. Given that the longest side of the polygon has a length of 6 cm and the perimeter of the polygon is 72 cm, find the value of d.
The answer is 0.2.
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1 solution
You can have 2 equations from A.P concept. Let "a" be the smallest side then 16th side will be "a+15d=6" (as the lenght of the 16th side is 6) and by summing all the sides you get "16a+(15*8)d=72"(As the perimeter of the polygon is 72). Now it is as easy as to solve this equations to get the value of " d". (Formula to get the second equation "(a) + (a+d) + (a+2d) + ... + (a+15d) = 72" )