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Geometry Level 1

If the line segment with length a a is parallel to the line segment with length x x In the diagram above, then what is the value of x ? x?

a + a b c a+\frac { ab }{ c } a + a c a b a+\frac { ac }{ ab } a + a c b a+\frac { ac }{ b } a + b c a a+\frac { bc }{ a }

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Vaibhav Prasad by Vaibhav Prasad , 21, India

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4 solutions

Since △ E C D ∼ △ B C A \triangle ECD \sim \triangle BCA and B A ∥ E D BA \parallel ED , we have

B A A C = E D D C \dfrac{BA}{AC}=\dfrac{ED}{DC} ⟹ \color{#D61F06}\large \implies x b + c = a b \dfrac{x}{b+c}=\dfrac{a}{b} ⟹ \color{#D61F06}\large \implies x = a ( b + c ) b = a b + a c b = a b b + a c b = x=\dfrac{a(b+c)}{b}=\dfrac{ab+ac}{b}=\dfrac{ab}{b}+\dfrac{ac}{b}= a + a c b \large \boxed{\color{#3D99F6}a+\dfrac{ac}{b}}

12 Helpful 0 Interesting 1 Brilliant 1 Confused
Thomas Siu
Mar 10, 2015

b a = b + c x \frac{b}{a} = \frac{b + c}{x}

b x = a b + a c bx = ab + ac

x = a + a c b x= a + \frac{ac}{b}

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Brian Mostoller
Feb 28, 2015

b/a = (b+c)/x bx=ab+ac x=a+ac/b

1 Helpful 0 Interesting 0 Brilliant 0 Confused

C O R R E C T ! CORRECT !

But try using latex :)

Vaibhav Prasad - 6 years, 3 months ago

or a/x=b/(b+c)

Nguyen Tra - 6 years, 3 months ago
Shubham Gurtu
Jun 25, 2017

Since two sides are parallel,ratio of their corresponding sides are similar. b/a = b+c/a x=a+ac/b

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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