Two sides of a triangle are 9 centimeters and 18 centimeters. which among the following is it's perimeter? A) 33cm B) 36cm C) 45cm D)54cm

Question

The answer is from the options

Answer 1

To form a triangle, the third side must be shorter than the sum of the other two sides, so the perimeter p=9+18+x where x is the length of the third side. x<9+18; 18<9+x; 9<18+x.

So x<27; x>9; x>-9. Therefore 9<x<27, hence the perimeter p must satisfy 36<p<54.

From the options, the only one that satisfies this inequality for p is option C.

CHECK

The three side lengths are 9, 18, 45-27, that is, 9, 18, 18. 9+18=27>18; 18+18>9, so the Triangle Rule is obeyed by this isosceles triangle.