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Geometry Level pending

In the adjoining figure, D E DE is parallel to B C BC and A D = 3 x − 2 , A E = 5 x − 4 , B D = 7 x − 5 AD=3x-2,AE=5x-4,BD=7x-5 and C E = 5 x − 3. CE=5x-3. Find the value of x . x.

only 1 1 10 7 \dfrac{10}{7} 1 1 or 7 10 \dfrac{7}{10} only 7 10 \dfrac{7}{10}

Ayush G Rai by Ayush G Rai , 20, India

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1 solution

Ayush G Rai
Jul 24, 2016

△ A D E \triangle ADE is similar to △ A B C . \triangle ABC. [According to A A A AAA property].
So, A D A B = A E A C ⇒ A D A D + D B = A E A E + E C \dfrac{AD}{AB}=\dfrac{AE}{AC}\Rightarrow \dfrac{AD}{AD+DB}=\dfrac{AE}{AE+EC}
⇒ \Rightarrow 3 x − 2 10 x − 7 = 5 x − 4 10 x − 7 \dfrac{3x-2}{10x-7}=\dfrac{5x-4}{10x-7}
⇒ \Rightarrow 3 x − 2 = 5 x − 4 ⇒ x = 1 3x-2=5x-4\Rightarrow x=\boxed1 only.

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