Question

In the given figure, PA, QB and RC are each perpendicular to AC. If AP=12cm, RC=4cm then find QB.​

Answer 1

$\huge\rm\underline\purple{Question :-}$

In the given figure, PA, QB and RC are each perpendicular to AC. If AP=12cm, RC=4cm then find QB.

$\huge\rm\underline\orange{Answer :-}$

Let ∠ RAC = α

and ∠ PCA = β

$\red{\underline\bold{To\: find,}}$

• Height, QB = ❓

$\blue{\underline\bold{We\: know\:,}}$

$\boxed{ \sf \purple{ tan\;θ\: =\frac{perpendicular}{base} }}$

$\green{\underline\bold{From\: the\:given\:figure,}}$

tan α = $\frac{h}{a}$

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

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

$\blue{\underline\bold{And,}}$

tan β = $\frac{h}{b}$

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

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

$\orange{\underline\bold{From\:these,}}$

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

$\pink{\underline\bold{Now, \:Dividing \:both\: sides \:by\: 'b'}}$

$\green{\underline\bold{We\:get,}}$

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

Let $\frac{a}{b}$ = 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

$\pink{\underline\bold{ ∴ \:The\:required\:answer\:,QB=\:3\: cm}}$

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Answer 2

Answer:

QB is equal to 3 cm..............