Question

In $△ACD$, AC= 8 cm, AD=4 cm and CE=6 cm. What is the length of BD?

• A. 3 cm
• B. 4 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is A 3 cm

$\text{Area of}△ACD=\frac{1}{2}\times \text{Base}\times \text{Height}$

$=\frac{1}{2}\times AD\times CE$

Also, considering AC as the base and BD as the height, we have:
$\text{Area of}△ACD=\frac{1}{2}\times AC\times BD$

$\therefore \frac{1}{2}\times AD\times CE=\frac{1}{2}\times AC\times BD$

i.e., $4\times 6=8\times BD$
$⟹BD=\frac{24}{8}cm$
Thus, $BD=3cm.$