The number of non-congruent integer-sided triangles whose sides b… - Vidyadip

MCQ

The number of non-congruent integer-sided triangles whose sides belong to the set $\{10,11,12, \ldots, 22\}$ is

A
$283$
B
$446$
✓
$448$
D
$449$

✓

Answer

Correct option: C.

$448$

c
(c)

We have,

Set $\{10,11,12, \ldots, 22\}$

Number of scalene triangle

$={ }^{13} C_3-3=283$

Number of isosceles triangle

$=\left({ }^{13} C_2 \times 2\right)-4=152$

Number of equilateral triangle

$={ }^{13} C_1=13$

So, total number of triangle

$=283+152+13=448$

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