SOLUTION: The side lengths of a quadrilateral produce an arithmetic sequence. If the longest side has a length of 24 cm and the perimeter is 60 cm, what are the other side lengths? Explain

Question 1081942: The side lengths of a quadrilateral produce an arithmetic sequence. If the longest side
has a length of 24 cm and the perimeter is 60 cm, what are the other side lengths?
Explain your reasoning.
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.
Mental solution

The average length of four sides is  = 15.


Now imagine 4 points in the number line, equidistantly placed with the step "d", which is the common difference of the AP.


Then the distance from the center to the fourth (right-most) point is 1.5d.


So, 1.5d = 24 - 15 = 9.   Hence,  d = 6.


Thus the sides are 24, 24-6 = 18, 18 - 6 = 12  and  12 - 6 = 6.


Answer.  The sides are 6, 12, 18 and 24 cm.

Check.   6 + 12 + 18 + 24 = 60 cm.

Solved (mentally, without equations).

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