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Question-13498




Question Number 13498 by sin (x) last updated on 20/May/17
Commented by ajfour last updated on 20/May/17
if △ABC is equilateral,  Area(△ABC)=12×Area(△AED).
$${if}\:\bigtriangleup{ABC}\:{is}\:{equilateral}, \\ $$$${Area}\left(\bigtriangleup{ABC}\right)=\mathrm{12}×{Area}\left(\bigtriangleup{AED}\right). \\ $$
Answered by mrW1 last updated on 21/May/17
since AE=EB  ⇒A_(ΔAEC) =A_(ΔBEC)   ⇒A_(ΔAEC) =(1/2)A_(ΔABC)   since DC=5×AD  ⇒A_(ΔCED) =5×A_(ΔAED)   ⇒A_(ΔAED) =(1/6)×A_(ΔAEC) =(1/6)×(1/2)A_(ΔABC)   ⇒A_(ΔABC) =12×A_(ΔAED) =12×4=48 cm^2     ⇒Answer ?)
$${since}\:{AE}={EB} \\ $$$$\Rightarrow{A}_{\Delta{AEC}} ={A}_{\Delta{BEC}} \\ $$$$\Rightarrow{A}_{\Delta{AEC}} =\frac{\mathrm{1}}{\mathrm{2}}{A}_{\Delta{ABC}} \\ $$$${since}\:{DC}=\mathrm{5}×{AD} \\ $$$$\Rightarrow{A}_{\Delta{CED}} =\mathrm{5}×{A}_{\Delta{AED}} \\ $$$$\Rightarrow{A}_{\Delta{AED}} =\frac{\mathrm{1}}{\mathrm{6}}×{A}_{\Delta{AEC}} =\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{1}}{\mathrm{2}}{A}_{\Delta{ABC}} \\ $$$$\Rightarrow{A}_{\Delta{ABC}} =\mathrm{12}×{A}_{\Delta{AED}} =\mathrm{12}×\mathrm{4}=\mathrm{48}\:{cm}^{\mathrm{2}} \\ $$$$ \\ $$$$\left.\Rightarrow{Answer}\:?\right) \\ $$
Commented by mrW1 last updated on 21/May/17
haha, clear! I had 12×3 in head.
$${haha},\:{clear}!\:{I}\:{had}\:\mathrm{12}×\mathrm{3}\:{in}\:{head}. \\ $$
Commented by mrW1 last updated on 21/May/17
Commented by ajfour last updated on 21/May/17
12×4≠36 .
$$\mathrm{12}×\mathrm{4}\neq\mathrm{36}\:. \\ $$
Commented by ajfour last updated on 21/May/17
i understand .
$$\mathrm{i}\:\mathrm{understand}\:. \\ $$

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