## anonymous 5 years ago 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?

1. anonymous

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

2. anonymous

How did you get the 80?

3. anonymous

66+14 = 80

4. anonymous

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.

5. anonymous

$x + \frac{2}{3}x + (x-14) = 66$ You can add the like terms, so you get$x + \frac{2}{3}x + x = \frac{3}{3}x + \frac{2}{3}x + \frac{3}{3}x = \frac{3+2+3}{3}x = \frac{8}{3}x$

6. anonymous

$\frac{8}{3}x - 14 = 66 \ \ , \frac{8}{3}x = 80 \ \ , 8x = 240 \ \ , x = 30$ Then solve for the other two sides.