A) 1 cm
B) 7 cm
C) 13 cm
D) None
Correct Answer: C
Solution :
[c] Let the sides of the triangle be \[a-d,\,\,a,\,\,a+d,\] then Perimeter \[=(a+d)+a+(a-d)=21\] \[\therefore \,\,\,a=7\] Again \[(a-d)\,\,(a+d)=a+6\] \[\Rightarrow \,\,\,{{a}^{2}}-{{d}^{2}}=a+6\Rightarrow 49-{{d}^{2}}=13\] \[\therefore \,\,\,\,d=\pm 6.\] Hence, the sides of the triangle are \[1\text{ }cm,\text{ }7\,cm,\text{ }13\,cm.\]
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