Question

# How many isosceles triangles with integer sides are possible such that sum of two of the side is 12

CAT 2021

Correct option is

**Explanatory Answer**

there can be two possibilities

Sum of the 2 equal sides = 12

sum of two unequal sides = 12

if sum of two equal sides were 12 , the sides should be 6 , 6 , x.

x could range from 1 to 11 .

11 integer values exist

now when 2 unequal sides add to 12, this could be 1 +11 , 2 +10 , 3 +9 , 4 +8 , 5 +7 .

isosceles triangle with the above combinations will be

{1, 11 ,11 } ,{2 , 10 ,10} , {3 , 9 ,9}, {4 , 8 , 8} , {5 , 7 ,7}, {5 , 5 ,7}

triplets such as {1,1,11} , {2,2,10} etc are eliminated as sum of the two smaller values is less than the largest value .

so , total possibilities are 11 + 6 = 17

hence , C is the correct option