SOLUTION: The perimeter of a quadrilateral​ (four-sided polygon) is 46 inches. The longest side is three times as long as the shortest side. The other two sides are equally long and ar

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Question 1061081: The perimeter of a quadrilateral​ (four-sided polygon) is 46 inches. The longest side is three times as long as the shortest side. The other two sides are equally long and are 2 inches longer than the shortest side. Find the length of all four sides.
Answer by ikleyn(52781) About Me  (Show Source):
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The perimeter of a quadrilateral​ (four-sided polygon) is 46 inches. The longest side is three times as long as the shortest side.
The other two sides are equally long and are 2 inches longer than the shortest side. Find the length of all four sides.
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Let x be the length of the shortest side in inches.

Then the longest is 3x inches long;
     the other two sides are (x+2) inches long.

Your equation is 

x + (x+2) + (x+2) + 3x = 42.   (the perimeter)

Simplify and solve for x. 

Can you complete the solution on your own from this point ?