समकोण `DeltaABC` में, `angleABC=90^(@)` , AB =3 , BC =4 , CA = 5 है। BN , भुजा AC पर लम्ब है। AN : NC है।

Options

A. `3:4`
B. `9:16`
C. `3:16`
D. `1:4`

Answer

B

Explanation

According to question
Given, `angleABC=90^(@)`
`(AN)/(NC)=?`

`DeltaABC-DeltaBNC`
`DeltaABC-DeltaANB`
`therefore DeltaABC-DeltaBNC-DeltaANB`
AB=3, BC=4, AC=5

`(AB)/(BN) = (AC)/(BC)`
BN=`(AB)xx(BC)/(AC) = (3xx4)/5 = 2.4`
`(BC)/(NC)=(AB)/(NB)`
`4/(NC)=3/2.4`
`NC=3.2`
`(AB)/(AN) = (BC)/(NB) = 3/AN = 4/2.4`
`therefore (AN)/(NC)=1.8/3.2=9/16`
Alternate
In such cases use the following method to save your valuable time.

`(AN)/(AC) = x^(2)/y^(2)`