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Question-177634




Question Number 177634 by aurpeyz last updated on 07/Oct/22
Answered by HeferH last updated on 07/Oct/22
    ((CD)/(AD)) = (1/3)    (A_1 /A_t )  = (1/9)⇒ ((42)/A_t ) = (1/9)   42∙9 = A_t  = 378
$$\: \\ $$$$\:\frac{{CD}}{{AD}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\: \\ $$$$\:\frac{{A}_{\mathrm{1}} }{{A}_{{t}} }\:\:=\:\frac{\mathrm{1}}{\mathrm{9}}\Rightarrow\:\frac{\mathrm{42}}{{A}_{{t}} }\:=\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\:\mathrm{42}\centerdot\mathrm{9}\:=\:{A}_{{t}} \:=\:\mathrm{378}\: \\ $$
Commented by aurpeyz last updated on 07/Oct/22
sorry. how did you get (1/9)?
$${sorry}.\:{how}\:{did}\:{you}\:{get}\:\frac{\mathrm{1}}{\mathrm{9}}? \\ $$
Commented by HeferH last updated on 07/Oct/22
When two triangles are similar,the ratio   of their areas is the ratio of their sides   squared. In this case    ((1/3))^2  = (1/9)
$${When}\:{two}\:{triangles}\:{are}\:{similar},{the}\:{ratio} \\ $$$$\:{of}\:{their}\:{areas}\:{is}\:{the}\:{ratio}\:{of}\:{their}\:{sides} \\ $$$$\:{squared}.\:{In}\:{this}\:{case}\:\:\:\:\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$
Commented by aurpeyz last updated on 09/Oct/22
thanks
$${thanks} \\ $$

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