The three sides of the described quadrangle are 4: 5: 3, find the smallest side if the perimeter is 28.

Let the consecutive sides of the quadrangle be equal: AB = 4 * X, BC = 5 * X, CD = 3 * X.

The sides AB and CD are opposite, then, by the property of the described quadrangle, the sum of its opposite sides is equal.

AB + CD = BC + AD.

4 * X + 3 * X = 5 * X + AD.

AD = 7 * X – 5 * X = 2 * X.

Then the perimeter of the quadrilateral is: Ravsd = AB + BC + CD + AD = 4 * X + 5 * X + 3 * X + 2 * X = 14 * X = 28.

X = 28/14 = 2.

The smaller side AD = 2 * X = 2 * 2 = 4 cm.

Answer: The smaller side is 4 cm.