The lengths of the sides of a triangle are 10 + x ^ 2 , 10 + x ^ 2...

Area of triangle, $\Delta = \sqrt{20\left(20 - 10 - {x}^{2}\right)\left(20 - 10 - {x}^{2}\right)\left(20 - 20 + 2{x}^{2}\right)}$

$\Delta = 2\sqrt{10}x\left(10 - {x}^{2}\right)$

For maxima, $\dfrac{d\Delta}{dx} = 0 ⇒ 2\sqrt{10}\left(10 - {x}^{2}\right) - 4\sqrt{10}{x}^{2} = 0$

$⇒ {x}^{2} = \dfrac{10}{3}$

Here, $\dfrac{{d}^{2} ∆}{d{x}^{2}} < 0$

Hence $3{k}^{2} = 10$