Question

In figure, $ABCD$ is a trapezoid in which $\overline{AB}$ is parallel to $\overline{CD},\overline{AD}$ is perpendicular to $\overline{DC}$, and $\overline{AD}$ is perpendicular to $\overline{AB}$. Calculate the length of $\overline{BC}$.

• A. $3$
• B. $4$
• C. $5$
• D. $6$
• E. $7$

Answer 1

The correct option is C $5$

In trapezoid $ABCD$, the $ABIICD$ and $AD$ perpendicular to $DC$ and $AD$ perpendicular to $AB$

And $AB=6,AD=4$ and $DC=9$

Draw perpendicular from $B$ on line $DC$ meet at point $E$.

Then $EC=DC-DE=9-6=3$ ( because $AB=DE=6$)

The in right angle $△BEC$

$\Rightarrow (BC{)}^2=(BE{)}^2+(EC{)}^2=(4{)}^2+(3{)}^2=16+9=25$

$\Rightarrow BC=\sqrt{25}=5$