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Question
The difference of any two sides of a triangle is always _______ than the third side.
The difference of any two sides of a triangle is always _______ than the third side.
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Solution
The correct option is B Lesser
We know that sum of any two sides of a triangle is always greater than the third side. So, in Δ ABC,
AB + BC > AC which gives AC – AB < BC
AB + AC > BC which gives BC – AC < AB
AC + BC > AB which gives AB – BC < AC
This means difference of any two sides of a triangle is always lesser than the third side.
Lesser
We know that sum of any two sides of a triangle is always greater than the third side. So, in Δ ABC,
AB + BC > AC which gives AC – AB < BC
AB + AC > BC which gives BC – AC < AB
AC + BC > AB which gives AB – BC < AC
This means difference of any two sides of a triangle is always lesser than the third side.
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