Question

If ∆ is the area of a triangle ABC and length of its two sides are 3 and 5. If c is the third side then-

• A. ∆ ≤ $\frac { c ^ { 2 } + 16 c + 64 } { 12 \sqrt { 3 } }$
• B. ∆ = $\frac { \mathrm { c } ^ { 2 } + 16 \mathrm { c } + 64 } { 8 }$
• C. ∆> $\frac { c ^ { 2 } + 16 c + 64 } { 4 \sqrt { 3 } }$
• D. None of these

Answer 1

Answer: (A)

∆ ≤ $\frac { c ^ { 2 } + 16 c + 64 } { 12 \sqrt { 3 } }$

Answer 2

[(s – a) (s – b) (s – c)]^1/3 ≤

⇒ ≤ $\frac { \mathrm { s } } { 3 }$ ⇒ ∆ ≤ $\frac { s ^ { 2 } } { 3 \sqrt { 3 } }$ = $\frac { c ^ { 2 } + 16 c + 64 } { 12 \sqrt { 3 } }$