`DeltaABC` में, `angleBAC=90^(@)` तथा `ADbotBC` है। यदि AD = 6 cm तथा BD = 4 cm हो, तब BC की लम्बाई ज्ञात करे?

Options

A. 8 cm
B. 10 cm
C. 9 cm
D. 13 cm

Answer

D

Explanation

According to question

Given: BAC is a right angle triangle (BAC एक समकोड़ त्रिभुज हैं )
`AD bot BC`
AD=6 cm
BD=4cm
BC=?
In `DeltaBAD`
`AB = sqrt(BD^(2) + AD^(2))`
`AB= sqrt(4^(2)+6^(2))` = `sqrt(52)` cm
`DeltaBAC ~DeltaBDA`

`therefore (BC)/(AB) = (AB)/(BD)`
`therefore (BC)/sqrt(52) = sqrt(52)/4`
`BC=52/4`
BC=13 cm
Alternate
`AB^(2) + BD.BC`
`sqrt(BD^(2)+AD^(2)) = BD.BC`
`sqrt(4^(2)+6^(2))=4.BC`
`52/4=BC`
`therefore` BC=13cm