त्रिभुज के चिन्हित स्थानों पर 1,2,3,4,5,6, को इस तरह लिखो जिससे प्रत्येक भुजा का योगफल 12 आये।
Answers
उतर :-
→ दी हुई संख्याएं है जो प्रयोग करनी है :- 1,2,3,4,5,6
त्रिभुज के चिन्हित स्थान माना A, B, C, D, E और F है l
अब,
- A + B + C = 12
- A + D + E = 12
- C + F + E = 12
- A = 4
- B = 2
- C = 6
- D = 3
- E = 5
- F = 1
देखने पर,
→ A + B + C = 12
→ 4 + 2 + 6 = 12
और,
→ A + D + E = 12
→ 4 + 3 + 5 = 12
और,
→ C + F + E = 12
→ 6 + 1 + 5 = 12
दूसरा संभव मान :-
→ A + B + C = 4 + 3 + 5 = 12
→ A + D + E = 4 + 2 + 6 = 12
→ C + F + E = 5 + 1 + 6 = 12
अत, हम कह सकते है कि, त्रिभुज के चिन्हित स्थानों पर इस प्रकार 1,2,3,4,5,6 लिखने पर हमें प्रत्येक भुजा का योगफल 12 प्राप्त होता है l
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Given : Triangle
numbers 1 to 6 are put at vertex and mid point of sides
Sum of each side of triangle is 12
To Find : How to place numbers
Solution:
Let say A , B , C are the the Vertex
and D , E and F are the mid points of AB , BC and AC respectively
A + D + B = 12
B + E + C = 12
A + F + C = 12
Adding all
=> (A + B + C + D + E + F) + A + B + C = 36
A + B + C + D + E + F = 1 + 2 + 3 + 4 + 5 + 6 = 21
=> 21 + A + B + C = 36
=> A + B + C = 15
with given Digits A + B + C = 15 is only possible
if A , B and C are 4 , 5 and 6 in any order
A = 4 , B = 5 C = 6
A + D + B = 12 => D = 3
B + E + C = 12 => E = 1
A + F + C = 12 => F = 2
Vertex are 4 , 5 , 6
mid points are 3 , 1 , 2
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