Question

If ∆ is area of ∆ABC and length of two sides are
3 & 5 respectively, if third side is c, then

• A. ∆ ≤$\frac{c^{2} + 16c + 64}{12\sqrt{3}}$
• B. ∆ = $\frac{c^{2} + 16c + 54}{8}$
• C. ∆>$\frac{c^{2} + 16c + 74}{4\sqrt{3}}$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

We know A.M. ≥ G.M.

∴$\frac{s - a + s - b + s - c}{3}$≥ $\sqrt[3]{(s - a)(s - b)(s - c)}$

⇒$\frac{s}{3}$ ≥ $\left( \frac{\Delta^{2}}{s} \right)^{1/3}$

∆ ≤ $\frac{s^{2}}{3\sqrt{3}}$

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