Question

15. The number of possible isosceles
triangles (excluding the case of
equilateral triangles) with integer
lengths of its sides such that the
sum of any two sides is 10, are
(a) infinite
(b) 16
(c) 13
(d) 8
​

Answer 1

the total number of triangle in this case will be eight

Answer 2

Answer:

Let the two equal sides of the isosceles triangle be x and the unequal side be y.

If x=5,y=0

Then,x+x=10

If x=5,y=1

Then,x+x=10

If x=5,y=2

Then,x+x=10

And so on.

Since y is an integer,

there are infinite values of y

And thus infinite number of isosceles triangles can be formed with the sum of any two sides 10.