Question

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Answer 1

Answer:

√7 will be the answer

Step-by-step explanation:

Refer the above attachment for your help

Its a long process in which I did so please understand everything carefully

Hope it helps

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:\triangle\:ABC=\sqrt{7}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies AB = AC \\ \\ \tt: \implies BD = BC = 2 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area \: of \: \triangle \: ABC = ?$

• According to given question :

$\tt : \implies AB= AC\\ \\ \tt\because ABC \sim BDC \\ \\ \tt: \implies \frac{AB}{BD} = \frac{BC}{DC} = \frac{AC}{BC} \\ \\ \tt: \implies cos \: A= \frac{ {x}^{2} + {x}^{2} - {2}^{2} }{2 \times x \times x} = \frac{ {2}^{2} + {2}^{2} - { (\frac{x}{2}) }^{2} }{2 \times 2 \times 2} \\ \\ \tt: \implies \frac{2 {x}^{2} - 4}{ {x}^{2} } = \frac{ 8 - \frac{ {x}^{2} }{4} }{4} \\ \\ \tt: \implies 8 {x}^{2} - 16 = {8x}^{2} - \frac{ {x}^{4} }{4} \\ \\ \tt: \implies \frac{ {x}^{4} }{4} = 64 \\ \\ \tt: \implies {x}^{4} = 64 \\ \\ \tt: \implies x = \sqrt[4]{64} \\ \\ \tt: \implies x = 2 \sqrt{2} \\ \\ \bold{For \: semiperimeter \: of \: \triangle \:ABC} \\ \tt: \implies s = \frac{2 \sqrt{2} + 2 \sqrt{2} + 2}{2} \\ \\ \tt: \implies s =2 \sqrt{2} + 1 \\ \\ \bold{For \: area \: of \: triangle} \\ \tt: \implies Area \: of \: \triangle \:ABC= \sqrt{s(s - a)(s - b) (s - c)} \\ \\ \tt: \implies Area \: of \: \triangle \:ABC= \sqrt{(2 \sqrt{2} + 1)(2 \sqrt{2} + 1 - 2)(2 \sqrt{2} + 1 - 2 \sqrt{2} )(2 \sqrt{2} + 1- 2 \sqrt{2} )} \\ \\ \tt: \implies Area \: of \: \triangle \: ABC= \sqrt{(2 \sqrt{2} + 1) (2 \sqrt{2} - 1)(1) (1) } \\ \\ \tt: \implies Area \: of \: \triangle \: ABC= \sqrt{4 \times 2 - 1} \\ \\ \green{ \tt: \implies Area \: of \: \triangle \: ABC= \sqrt{7} }$