Question

How many different (mutually non-congruent) trapezium s can be constructed using four distinct side lengths from the set $\left\{1,2,3,4,5,6\right\}$ ?

• A. 5
• B. 11
• C. 15
• D. 30

Answer 1

Answer: (B)

Length of sides of trapezium from $\left\{1,2,3,4,5,6\right\}$
From non-congruent trapezium
$|r-p|<q+s<r+p$
Possible combination are
$\left(r,p\right),\left(s,q\right)\equiv \left\{\left(5,6\right),\left(1,3\right)\right\},\left\{\left(5,6\right),\left(2,4\right)\right\}$
$\left\{\left(5,6\right),\left(1,4\right)\right\},\left\{\left(5,6\right),\left(3,4\right)\right\},\left\{\left(6,4\right),\left(1,3\right)\right\}$,
$\left\{\left(6,4\right),\left(1,5\right)\right\},\left\{\left(6,4\right),\left(2,3\right)\right\},\left\{\left(6,4\right),\left(3,5\right)\right\}$,
$\left\{\left(4,5\right),\left(1,3\right)\right\}\left\{\left(4,5\right),\left(1,6\right)\right\}\left\{\left(4,5\right),\left(2,6\right)\right\}$
Total $11$ combination is possible