How many equilateral triangles are possible whose sum of squares of any two sides
are 16?
ऐसेदकतने
Answers
Step-by-step explanation:
If we represent equal sides of given isosceles triangle as A & A & the third side as B .
Since, given that the sum of its 2 sides = 12 , So
[1]st case A+A = 12
[2]nd case A + B = 12
IF A + A = 12 …………★
=> A = 6,
& B < A+A
= B < 12 (but excluding 0 & negative integers)
& if B = 6 , in that case the isosceles triangle becomes equilateral..
B = 1,2,3,4,5,6,7,8,9,10,11
So, here 11such isosceles triangles are possible…………(●)
IF A+ B = 12 …………..★
B< 8 ( b'coz , A+A> B& A+B=12)( B excludes 0, & negative integers)
So, (A,B) will be (11,1)(10,2),(9,3)(8,4)(7,5),(6,6), (5,7)
And here 7 such triangles are possible………..●
TOTAL 16 isosceles triangles are possible
PS!
Case 1 :
(6,6,1) (6,6,2), (6,6,3), (6,6,4), (6,6,5), (6,6,6), (6,6,7), (6,6,8) (6,6,9), (6,6,10),(6,6,11) = 11 triangles
Case2: (11,1,11), (10,2,10), (9,3,9), (8,4,8), (7,5,7),(6,6,6) (5,7,5) = 6 triangles (as 6,6,6 triangle has been included)
TOTAL = 17 triangles