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Question Number 124522 by bemath last updated on 03/Dec/20

Answered by mr W last updated on 04/Dec/20

CD=25−16=9  AC^2 =BC×CD=16×9  AC=4×3=12  AB^2 =BC^2 +AC^2 =16^2 +12^2   AB=(√(16^2 +12^2 ))=20  ((AE)/(AC))=((AC)/(AB))  ⇒AE=((12^2 )/(20))=7.2  ⇒answer D

$${CD}=\mathrm{25}−\mathrm{16}=\mathrm{9} \\ $$$${AC}^{\mathrm{2}} ={BC}×{CD}=\mathrm{16}×\mathrm{9} \\ $$$${AC}=\mathrm{4}×\mathrm{3}=\mathrm{12} \\ $$$${AB}^{\mathrm{2}} ={BC}^{\mathrm{2}} +{AC}^{\mathrm{2}} =\mathrm{16}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} \\ $$$${AB}=\sqrt{\mathrm{16}^{\mathrm{2}} +\mathrm{12}^{\mathrm{2}} }=\mathrm{20} \\ $$$$\frac{{AE}}{{AC}}=\frac{{AC}}{{AB}} \\ $$$$\Rightarrow{AE}=\frac{\mathrm{12}^{\mathrm{2}} }{\mathrm{20}}=\mathrm{7}.\mathrm{2} \\ $$$$\Rightarrow{answer}\:{D} \\ $$

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