Question

In the given figure, if AB = 15 cm, then the value of (AC – BC) is

• A. 4.5 cm
• B. 6 cm
• C. 10.5 cm
• D. 12 cm

Answer 1

The correct option is B 6 cm


As,
$\Delta AA,C-\Delta B{B}_{3}C$
$\therefore \frac{A{A}_7}{B{B}_3}=\frac{AC}{BC}$
(Ratio of similar triangles are equal)

Since,by construction,$\frac{A{A}_7}{B{B}_3}=\frac{7}{3}$,
$\therefore \frac{AC}{BC}=\frac{7}{3}$
Thus, $AC=\frac{7}{3}BC$

Now,
$AC-BC=\frac{7}{3}BC-BC=\frac{4}{3}BC$.......(i)

Now, $AB=AC+BC=15cm$
$\Rightarrow AC+BC=\frac{7}{3}BC+BC=15$

$\Rightarrow \frac{10}{3}BC=15$

$\Rightarrow BC=4.5cm$.......(ii)

From (i) and (ii)
$AC-BC=\frac{4}{3}\times 4.5$
$=\frac{18}{3}$
$=6cm$
Hence,the correct answer is option b.