Question

Find BC, if AB = 7.2 cm.

• A. $7.2cm$
• B. $7.1cm$
• C. $0.72cm$
• D. $72cm$

Answer 1

The correct option is A $7.2cm$

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, $△ACE\sim △BCD$ BY AAA similarity criterion.

Thus, $\frac{BC}{AC}=\frac{CD}{CE}$

$\Rightarrow \frac{BC}{BC+AB}=\frac{CD}{CD+DE}$

Given that, $CD=DE$

Hence, $\frac{BC}{BC+AB}=\frac{1}{2}$

$\Rightarrow 2BC=AB+BC$

$\therefore BC=AB$

$\Rightarrow BC=7.2cm$.

Hence, $BC=7.2cm$