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15. If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 8 III. 11 (A) ?I only (B) ?II only (C) I and ?I only (D) II and ?II only (E) I, ??, and ???

Plz explain. Thanks

the rest side x must satisfy : 8-3<x< 8+3 <==> 5<x<11
B.

Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?

I don't quite understand what you mean by the red part above. Anyway:

If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I. 5 II. 8 III. 11

(A) ΙI only (B) ΙII only (C) I and ΙI only (D) II and ΙII only (E) I, ΙΙ, and ΙΙI

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, \((8-3)<x<(8+3)\) --> \(5<x<11\). Hence 5 and 11 cannot be the length of the third side, while 8 can be.

If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 8 III. 11 (A) ?I only (B) ?II only (C) I and ?I only (D) II and ?II only (E) I, ??, and ???

Since the new side has to be less than the sum of the other two sides

Choosing 5 -
3, 8 is not possible as 3+5 leads to 8 - so the other side will have to be less than 8 (but we know it is 8). So 5 is not a correct side.

Choosing 8 -
3, 8, 8 is still valid - (isosceles triangle if I still remember how to spell those) as the sum of any two is still bigger than the other side.

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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