The sides of a triangle are distinct positive | vedclass

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Question

(b)

Let the sides be $a, b, c$ which are in A.P. with $c$ as the smallest.

$	herefore c =10$

$	herefore a , b > 10$

$	herefore 2 b =

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(b) Let the sides be $a, b, c$ which are in A.P. with $c$ as the smallest. $ herefore c =10$ $ herefore a , b > 10$ $ herefore 2 b = a + c = a +10$ $ herefore b + c > a$ $\Rightarrow b +10 > a$ From eq $(1)$ and $(2)$: $\Rightarrow b +10 > 2 b -10$ $\Rightarrow b < 20$ $ herefore 10 < b < 20$ $ herefore$ No. of possible values of $b=9$ $ herefore$ No. of triangles possible $=9$

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

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