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Question Number 187524 by sonukgindia last updated on 18/Feb/23

	Answered by HeferH last updated on 18/Feb/23

	Commented by HeferH last updated on 18/Feb/23

	$A r e a o f t r i a n g l e (\sqrt{20}, \sqrt{20}, \sqrt{8}) = A$ $A = \sqrt{s (s - a) (s - b) (s - c)} (H e r o n)$ $A = \sqrt{(2 \sqrt{5} + \sqrt{2}) (\sqrt{2}) (\sqrt{2}) (2 \sqrt{5} - \sqrt{2})}$ $A = \sqrt{(20 - 2) 2} = 6$ $b u t a l s o : A = \frac{2 \sqrt{5} \cdot h}{2} = 6$ $h = \frac{6}{\sqrt{5}} = \frac{6 \sqrt{5}}{5}$ $a^{2} = r^{2} - h^{2}$ $a^{2} + {(r - h)}^{2} = x^{2}$ $2 r^{2} - 2 r h = x^{2}$ $2 (20) - 2 \sqrt{20} \cdot \frac{6 \sqrt{5}}{5} = x^{2}$ $40 - 24 = x^{2}$ $16 = x^{2}$
	Commented by HeferH last updated on 18/Feb/23

	Answered by mr W last updated on 18/Feb/23

	Commented by mr W last updated on 18/Feb/23

	${(\sqrt{2} \sqrt{20})}^{2} = s^{2} + {(\sqrt{8})}^{2} + 2 s \times \sqrt{8} \times \frac{\sqrt{2}}{2}$ $s^{2} + 4 s - 32 = 0$ $(s - 4) (s + 8) = 0$ $\Rightarrow s = 4$ $a r e a o f s q u a r e s^{2} = 16$
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