How many quadrilaterals

Geometry Level 2

Joy has $33$ thin rods, one each of every integer length from $1$ cm through $30$ cm, and also three more rods with lengths $3$ cm, $7$ cm, and $15$ cm. She places those three rods on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?

The answer is 19.

1 solution

Sharky Kesa
Aug 19, 2017

Let the 4th side be equal to $x$ . By triangle inequality (applied to a quadrilateral), we have $x+3+7 > 15$ , so $x\geq 6$ . Also, we have $x < 3+7+15$ , so $x\leq 24$ . Thus, there are $24-6+1 = 19$ rods satisfying.

How many quadrilaterals

The answer is 19.

1 solution

0 pending reports