Question

The sides of a triangle are distinct positive integers in an arithmetic progression.If the smallest side is 10, the number of such triangles is

• A. $8$
• B. $9$
• C. $10$
• D. infinitely many

Answer 1

Answer: (B)

$9$

Let the sides be $a,b,c$ which are in A.P. with c as the smallest.

$\therefore c=10$

$\therefore a,b>10$

$\therefore 2b=a+c=a+10$ ...( 1 )

$\therefore b+c>a$

$\Rightarrow b+10>a$ ...( 2 )

From eq (1) and (2):

$\Rightarrow b+10>2b-10$

$\Rightarrow b<20$

$\therefore 10<b<20$

$\therefore$ No. of possible values of b $=9$

$\therefore$ No. of triangles possible $=9$