Math, asked by mrrcsutha, 3 months ago

How many equilateral triangles are possible whose sum of squares of any two sides

are 16?

ऐसेदकतने​

Answers

Answered by tanishgupta886
1

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

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