question_answer

Find the maximum area that can be enclosed in a triangle of perimetre 24 cm:

A) \[32\,c{{m}^{2}}\]               

B)        \[16\sqrt{3\,}c{{m}^{2}}\]

C) \[16\sqrt{2\,}\,c{{m}^{2}}\]          

D)       \[27\,c{{m}^{2}}\]

E) None of these

Correct Answer: B

Solution :

Explanation Option [b] is correct. For the given perimetre of a triangle the maximum area is enclosed by an equilateral triangle. \[\therefore 3a=24cm\] \[\Rightarrow a=8cm\] \[\therefore Area\,=\,\frac{\sqrt{3}}{4}{{a}^{2}}=\frac{\sqrt{3}}{4}\times {{(8)}^{2}}=16\sqrt{3}\,c{{m}^{2}}\]