A triangle has two sides which are 9 cm and 12 cm in lengths, respectively. Anna says that the third side could be 3 cm. Mary say that it could not be 3 cm but it could be 13 cm. Who is correct and why?
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Answers
Answer :
Mary said correctly
13 cm
Given :-
A triangle has two sides which are 9 cm and 12 cm in lengths, respectively. Anna says that the third side could be 3 cm. Mary say that it could not be 3 cm but it could be 13 cm.
To find :-
Who is correct and why?
Solution:-
Given that:
The two sides of a triangle are 9 cm and 12 cm
We know that
By Inequalities of a triangle:
The sum of any two sides of a triangle is greater than the third side
9+12 = 21 cm
And
The difference between two sides is Less than the third side
12-9 = 3 cm
So the length of the third side must be lie between 21 cm and 3 cm
3cm < third side < 21 cm
So, According to this
Anna said wrong because
9+3 = 12 cm
The sum of two sides is not greater than the third side 12 cm
And
Mary said correct
9+13 = 21 cm > 12 cm
The sum of two sides is greater than the third side 12 cm
Answer:-
Mary said correctly
The length of the third side of the triangle could be 13 cm
Used formulae:-
Inequalities of a triangle:-
- The sum of the lengths of any two sides of a triangle is greater than the third side.
- The difference between the lengths of the two sides is Less than the third side