किसी `DeltaABC` की दो माध्यिकाएं AD एवं B E, बिंदु G पर समकोण पर विभाजित होती है । यदि AD=9cm तथा BE=6cm हो , तब BD की लम्बाई cm में ज्ञात करे ?

Options

A. 10
B. 6
C. 5
D. 3

Answer

C

Explanation

According to question

G is the centroid which divides the median in `2:1`
`therefore AD=3`units = 9cm
1 unit =`9/3=3cm`
`therefore` GD=3cm
BE=3 units =6cm
3units =6cm
1unit =`6/3`
2units = `6/3 xx 2 = 4cm`
`therefore BG = 4cm`
`DeltaBDG` is a right angle triangle
`BD^(2) = BG^(2)+GD^(2)`
`BD^(2) = (4)^(2)+(3)^(2)`
`BD^(2)=16+9`
BD = `sqrt(25)`
BD=5cm