MCQ
How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1,2,3,4,5,6\}$ ?
- A$5$
- ✓$11$
- C$15$
- D$30$
✓
Answer
Correct option: B.
$11$
b
(b)
(b)
Length of sides of trapezium from $\{1,2,3$, $4,5,6\}$.
From non-congruent trapezium
$|a-c| < b+d < a+c$
Possible combination are
$(r, p),(s, q) \equiv\{(5,6),(1,3)\},\{(5,6),(2,4)\}$
$\{(5,6),(1,4)\},\{(5,6),(3,4)\},\{(6,4),(1,3)\}$,
$\{(6,4),(1,5)\},\{(6,4),(2,3)\},\{(6,4),(3,5)\}$
$\{(4,5),(1,3)\}\{(4,5),(1,6)\}\{(4,5),(2,6)\}$
Total $11$ combination is possible.
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