For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.)
A) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x ^ { 2 } }$
B) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x }$
C) $A B ( x ) = \frac { ( x + 3 ) \sqrt { x + 4 } } { x }$
D) $A B ( x ) = \frac { ( x + 3 ) ^ { 2 } ( x + 2 ) } { x }$
E) $A B ( x ) = \frac { ( x + 3 ) \left( x ^ { 2 } + 2 \right) } { x }$

Question

For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.) 
A) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x ^ { 2 } }$ 
B) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x }$ 
C) $A B ( x ) = \frac { ( x + 3 ) \sqrt { x + 4 } } { x }$ 
D) $A B ( x ) = \frac { ( x + 3 ) ^ { 2 } ( x + 2 ) } { x }$ 
E) $A B ( x ) = \frac { ( x + 3 ) \left( x ^ { 2 } + 2 \right) } { x }$

Quizplus · Accepted Answer

We can see that triangle ABC and triangle ABD are similar.

$\dfrac{AB}{AD}=\dfrac{BC}{BD}$

$\dfrac{AB}{x+3}=\dfrac{\sqrt{x^2+9}}{x}$

$AB=\dfrac{(x+3)\sqrt{x^2+9}}{x}$

Simplifying this expression, we get

$AB=\dfrac{(x+2)\sqrt{x^2+9}}{x}$

So, the answer is choice B.

For the Following Figure, Express the Length AB as a Function