Question

In the adjoining figure $AB=12cm,CD=8cm,\angle ABD=\angle AEC\angle EDC={90}^{\circ }$ . If $BE=x,$ then

• A. $x$ has two possible values whose difference is $4$
• B. $x$ has two possible values whose sum is $28$
• C. $x$ has only one value and $x\ge 12$
• D. $x$ cannot be determined with the given information

Answer 1

The correct option is A $x$ has two possible values whose difference is $4$

$\frac{12}{x}=\frac{20-x}{8}$
$\Rightarrow x^2=20x+96=0$
$x=8,12$