minimum perimeter of a triangle

[defeated_soldier]

How to solve this question ?

what is the minimum value of the perimeter of a triangle , two of whose sides are 5 cm and 7 cm ?
(the sides have integer values)
a) 9 cm
b)13 cm
c)14cm
d)15 cm

 

[tkhunny]

Ever hear of the "Triangle Inequality"?

http://mathworld.wolfram.com/TriangleInequality.html

 

[defeated_soldier]

Ever hear of the "Triangle Inequality"?

http://mathworld.wolfram.com/TriangleInequality.html

thanks for the link..

It says

the triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

that means third side<5+7 =>third side<12

so, whats the value of third side then ? is it 11 ? is it 10 ? is it 9 ? or what ?

This law fails to tell me the exact value of third side.


N.B:

solution in my book:
the minimum length of the third side is 3 cm
so, the minimum value of the perimeter is =15 cm

i dont understand this solution...can you pleae explain how it works ?

Thank you

 

[stapel]

Just follow the definitions and the logic:

What is the sum of the other two sides?

What value, then, must the third side be greater than?

What is the smallest (minimum) integer greater than this value?

Eliz.

 

[defeated_soldier]

Just follow the definitions and the logic:

What is the sum of the other two sides?

What value, then, must the third side be greater than?

What is the smallest (minimum) integer greater than this value?

Eliz.

Thanks for the great Tips.

5+7>x
7+x>5
5+x>7

thee eqn leades to 12>x>2

so the min value of x is 3


Thank you