Question

in the right triangle ABC, angle A=90 and AD perpendicular BC .Then BD/DC=?...option (a) (AB/AC)square (d)(AB/AC) (C)(AB/AD)SQUARE (D)AB/AD....WHICH OF THE FOLLOWING ANSWER IS RIGHT?​

Answer 1

Answer = AB/AC=BD/DC

Option b

Please give 5

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Answer 2

The correct answer is option (a)

$\frac{ {AB}^{2} }{ {AC}^{2} }$

GIVEN

ABC is ∆

∠A = 90°

AD⏊BC

TO FIND

$\frac{BD}{DC}$

SOLUTION

We can simply solve the above problem as follows-

In ΔABC and ΔDBA

∠BAC = ∠DAB = 90°

∠ABC = ∠DBA (Common angle)

Therefore,

ΔABC ≈ ΔDBA (By A-A similarity criterion)

So,

$\frac{AB}{AC} = \frac{DB}{AD}$

$AD = \frac{BD \times AC}{AB}$

In Δ ABD and ΔADC

∠DAB = ∠ACD (Third angles of similar triangle)

∠ADB = ∠ADC = 90°

Therefore,

Δ ABD ≈ ΔADC

SO,

$\frac{AB}{AC} = \frac{AD}{CD}$

$AD = \frac{AB \times \: CD}{AC}$

Comparing the value of AD -

$\frac{BD \times AC}{AB} = \frac{AB \times \: CD}{AC}$

$\frac{BD}{CD} = \frac{ {AB}^{2} }{ {AC}^{2} }$

Hence, The correct answer is option (a)

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