Chapter 13.5, Problem 16PPS

To determine

To determine probability that the quadrilateral is a rhombus.

Answer to Problem 16PPS

Probability is $\frac{1}{5}.$

Explanation of Solution

Given information:

Perimeter of the quadrilatoral is 12.

Side is odd.

Total numbers of possibilities of getting perimeter 12, by 4 odd sides are,

(3+3+3+3), (1+1+1+9), (1+1+5+5), (1+1+3+7), (1+3+3+5)

Hence there are only 5 possibilities.

We know that all sides of rhombus are equal.

Hence we have only 1 possibility from total 5.

Hence the probability is $\frac{1}{5}$ .