question_answer

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

A) \[32c{{m}^{2}}\]

B) \[16\text{ }\sqrt{3}\text{ }c{{m}^{2}}\]

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

D) \[27\text{ }c{{m}^{2}}\]

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 = 24 cm \[\Rightarrow \]   a = 8 cm           \[\therefore \]      Area \[=\frac{\sqrt{3}}{4}{{a}^{2}}=\frac{\sqrt{3}}{4}\times {{(8)}^{2}}=16\sqrt{3}\,\,c{{m}^{2}}\]