Question

In the given figure, PA, QB and RC are each
perpendicular to AC. If AP = 12 cm, RC = 4 cm then
QB = ?
(A) 2 cm
(B) 3 cm
12 cm
(C) cm
(D) 4 cm
14 cm
a cm
b cm
C​

Answer 1

Answer:

3 cm

Step-by-step explanation:

Let

$\angle RAC = \alpha \: \: \: and \: \: \: \angle \: PCA= \beta$

Observe

$\tan( \alpha ) = \frac{h}{a} = \frac{4}{a + b} \\ \tan( \beta ) = \frac{h}{b} = \frac{12}{a + b}$

from these

$h = \frac{4a}{a + b} = \frac{12b}{a + b} \\ \\ h = \frac{4 \frac{a}{b} }{1 + \frac{a}{b} } = \frac{12}{ \frac{a}{b} + 1}$

Let a/b = x

$h = \frac{4x}{x + 1} = \frac{12}{1 + x}$

$\frac{4x - 12}{x + 1} = 0 \\ x = 3$

So

$h = \frac{12}{x + 1} = \frac{12}{4} = 3$