Question Specific: Question 8 in Test 2, Section 2 of BigBook.

The Question asks us the bigger quantity between ‘x+y’ and ‘z’, where x,y and z are sides of a triangle. No other data is provided.

My answer to this question is D because, x+y>=z as per triangle property. So x+y can be greater or equal to z. However, the answer key shows the answer as A. Can you please help me understand where I am going wrong?

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It is not equal means x+y >z , correct idea is sum of any two sides is greater than the third side. So applying this you will get A

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Yes I took this into account. Just one follow-up on the same. Will the same hold for an isosceles triangle?

Yes it is basic for every triangle

third side of a triangle must be followed by this rule : x~y < z < x+y .that is why the answer is A

Yes because if x + y = z the triangle becomes a line.

same for x - y = z that is also a line.

To illustrate this I think of a number line. If x is the distance between 0 and 2 and y is the distance between 2 and 5 and z equals x + y then clearly it’s a line and cannot a be a triangle.