The ratio of the side lengths of a quadrilateral is 2:3:5:6 and its perimeter is 48 cm. What is the length of the longest side?

The side lengths are given in proportions which are 2:3:5:6. The perimeter is given as the sum of all the sides which is given as 48 cm. Using ratio and proportion, the sum of all the sides or the perimeter is proportional to the sum of all the fractions and the largest fraction is proportional to the longest side of the quadrilateral.

Let x be the longest side of the quadrilateral. The largest proportion is 6.

6 / (2+3+5+6) = 6/16

6/16 = x/48

x = 18 cm. The longest side is 18 cm. The other sides are 6, 9, 15 using the other proportions.