in how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected
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The number of pairs of diagonals of a regular polygon of `10` sides that are parallel are
The number of pairs of diagonals of a regular polygon of `10` sides that are parallel are A. `45` B. `56` C. `22` D. `64`
10 10
sides that are parallel are
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The number of pairs of diagonals of a regular polygon of 10 sides that are parallel are
(a) Fix a vertex A. There are 4 parallel diagonals. There are 5 such sets since the vertices of the 10-gon can be paired into 5 sets. In each set there are "^(4)C(2) pairs, i.e, a total of "^(4)C(2)xx5=30 pairs of diagonals. Now fix a side AB. There are 3 parallel diagonals and 5 such sets. So, total pairs =^(3)C(2)xx5=15 Hence, net total =30+15=45
The number of pairs of diagonals of a regular polygon of
10
sides that are parallel are
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Updated On: 27-06-2022
Text Solution A 45 B 56 C 22 D 64 Answer
The correct Answer is A
Solution ( a )
Fix a vertex A . There are 4 parallel diagonals. There are 5
such sets since the vertices of the
10
-gon can be paired into
5
sets. In each set there are
4 C 2
pairs, i.e, a total of
4 C 2 × 5 = 30 pairs of diagonals. Now fix a side A B . There are 3
parallel diagonals and
5 such sets. So, total pairs = 3 C 2 × 5 = 15 Hence, net total = 30 + 15 = 45 Answer
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यदि एक नियमित बहुभुज में भुजाओं की संख्या 10 है तो विकर्णों की संख्या होगी?
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645006448 Text Solution
The number of pairs of diagonals of a regular polygon of
10
sides that are parallel are
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In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected?
Answer (1 of 2): There are diagonals that are parallel to a side, and diagonals that aren’t parallel to a side of the polygon. First we look at diagonals parallel to a side of the polygon There are 5 pairs of opposite sides, and each of these pairs is parallel. For each of these pairs you have...
In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected?
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Sort Jacob Sarkar
Studying('21-'23expected) from Ramakrishna Mission Vidyapith, DeogharAuthor has 155 answers and 146.8K answer views2y
Here, for 10 sided polygon….
So, let's know the formula first….
This proof was shown by Sir Doug Dillon as answer to the question How do I find the number of parallel diagonals in a polygon?
Now, let's come to this problem
So answer is 45 pairs…
Note- A decagon has n(n+3) n(n+3) = 35 35 diagonals diagonals
But, one diagonal may form the parallel pair with more than one diagonal!!!
✍️ Jacob Sarkar.
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There are diagonals that are parallel to a side, and diagonals that aren’t parallel to a side of the polygon.
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:-)
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Guys, does anyone know the answer?