Question

How to solve his problem.

The sides of a triangle are distinct positive integers in an AP.If the smallest side is 10 then the no.of such triangles is?

Answer 1

let the number be x-d ,x and x+d .

Now smallest number is 10 .

⇒x-d =10

Now diff. between two sides is always smaller than the third side .

i.e. (x+d) - x < 10

⇒ d < 10.

Now as the number are distinct positive integer so d can lie between 1 to 9 i.e 9 value

So the number of such possible sets are 9 .These are {10,11,12},{10,12,14},{10,13,16}......{10,19,28}