Question

Solve question number 2 properly pls fast pls


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Answer 1

$\green{\underline{\huge{Solution}}}$

$\red{Here\: \angle{DAC} \:is\: exterior \:angle \: and \:AE \:bisect \:the \:angle \:so\: that}$

$\red{\boxed{\angle DAE = \angle CAE}}$

$In\: \triangle ACB , \:AE\: is \:the\: bisector\: of \angle DAC , \:the\: internal\: bisector$ $of \:an \:angle \:of \:a\: triangle\: divides \:the\: opposite \:side \:internally$ $in \:the \:ratio\: of\:sides \:containing \:the \:angle$

$Now\: we \:take \:sides\:in\:ratio\colon\\\implies \frac{BE}{EC}=\frac{BA}{CA}\\ \implies \frac{12+x}{x}= \frac{10}{6}\\\implies 6(12+x)=10x\\\implies 72+6x=10x\\\implies 10x-6x=72\\\implies 4x=72\\\implies x=\frac{\cancel 72}{\cancel 4} \\\implies x = 18 cm$

Now , you get a answer

$\red{\underline{Answer}}$

$\boxed{\orange{\bold{ x \:=\: 18 cm }}}$