August 2018 Geometry#5

Geometry Level pending

In the above figure, F E ∥ A D FE\parallel AD and F D ∥ A C FD\parallel AC .

If B E = 3 BE =3 , D C = 5 DC =5 , and E D = x ED = x , then find the value of ( 2 x + 3 ) 2 (2x+3)^2 .


The answer is 69.

Vaibhav Priyadarshi by Vaibhav Priyadarshi , 17, India

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1 solution

X X
Aug 10, 2018

B D ‾ : D C ‾ = B F ‾ : F A ‾ = B E ‾ : E D ‾ \overline{BD}:\overline{DC}=\overline{BF}:\overline{FA}=\overline{BE}:\overline{ED}

So ( x + 3 ) : 5 = 3 : x (x+3):5=3:x ,solving and get ( 2 x + 3 ) 2 = 69 (2x+3)^2=69

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