Question

Find $BC$, if $AB=7.2cm$.

• A. $7.2$
• B. $6.4$
• C. $5.2$
• D. $4.2$

Answer 1

The correct option is A $7.2$

In $△ACE$ and $△BCD$,
$\angle ACE=\angle BCD$ (Common angle)
$\angle CBD=\angle CAE$ (Corresponding angles, since $BD||AE$)
$\angle CDB=\angle CEA$ (Corresponding angles, since $BD||AE$)
Hence, $△ACE\sim △BCD$.

Thus, $\frac{BC}{AC}=\frac{CD}{CE}$
$⟹$ $\frac{BC}{BC+AB}=\frac{CD}{CD+DE}$ (Given, $CD=DE$)
$⟹$ $\frac{BC}{BC+AB}=\frac{1}{2}$
$⟹$ $2BC=AB+BC$
$⟹$ $BC=AB$
$⟹$ $BC=7.2cm$.

Hence, option $A$ is correct.