Question

The ratio of the side lengths of a quadrilateral is 3:2:6:7, and its perimeter is 126 meters. What is the length of the shortest side?

Answer 1

since the lengths of all those four sides are in a 3:2:6:7 ratio, and the whole perimeter is 126, what we do is, simply divide the whole by (3+2+6+7) and distribute accordingly.

$\bf \stackrel{3\cdot \frac{126}{3+2+6+7}}{3}~~:~~\stackrel{2\cdot \frac{126}{3+2+6+7}}{2}~~:~~\stackrel{6\cdot \frac{126}{3+2+6+7}}{6}~~:~~\stackrel{7\cdot \frac{126}{3+2+6+7}}{7} \\\\\\ 3\cdot \cfrac{126}{18}~~:~~2\cdot \cfrac{126}{18}~~:~~6\cdot \cfrac{126}{18}~~:~~7\cdot \cfrac{126}{18} \\\\\\ 21~~:~~\stackrel{shortest}{14}~~:~~42~~:~~49$