Question

how many isosceles triangle are there such that each of its sides has an intergral length and its perimer is 144​

Answer 1

Step-by-step explanation:If the sides of the isosceles triangle are a , a , b , we must have 2a+b=144 with a,b∈N and b<2a . Thus, b=144–2a<2a , so that a>36 , and 2a<144 , so that a<72 . We must exclude the case a=b , for that gives an equilateral triangle. Since a=b implies a=48 , a∈{37,38,39,…,71}∖{48} .

There are 71–37=34 isosceles triangles with integer sides and perimeter 144