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A triangular region has a perimeter of 66 meters. The first side is two-thirds of the second side. The third side is 14 meters shorter than the second side. What are the lengths of the three sides of the triangular region?

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let second side = x meter, first side = 2x/3 meter and third side = x-14 sum of all sides i.e perimeter x +2x/3 + x-14 = 66 => 2x+2x/3 =80 =>8x/3 =80 => x = 30 so, first side = 20 meters, second side = 30 meters third side = 16 meters
How did you get the 80?
66+14 = 80

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How do you eliminate the fraction? 2/3x I thought you should multiply both sides of the equation by the least common denominator. Thanks for the explanation.
\[x + \frac{2}{3}x + (x-14) = 66\] You can add the like terms, so you get\[x + \frac{2}{3}x + x = \frac{3}{3}x + \frac{2}{3}x + \frac{3}{3}x = \frac{3+2+3}{3}x = \frac{8}{3}x\]
\[\frac{8}{3}x - 14 = 66 \ \ , \frac{8}{3}x = 80 \ \ , 8x = 240 \ \ , x = 30\] Then solve for the other two sides.

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