Question

in triangle ABC
<ABC=90°
AD=12cm
DC=25cm
BD is perpendicular to AC
then BD =????
1. 8 root 5
2. 12 root 3
3. 12 root 2
4. 10 root 3
Please answer !!

Answer 1

in right angle triangle the DCB USING PYTHAGORAS theorerm....
BD²+DC²=BC²

BD² = BC² - DC²
BD² = BC² - 25²

then BC>25
BC<BD

similarly in ∆BDA
AB²=BD²+AD²
BD²=AB²-AD²
BD²=AB²-144

then AB>12
AB>BD
then AB < BC
then
BD exists less than 12
so option B & C cannot be the answer
trial and error method by putting 8√3 and 10√3 for both triangles ABD & BAC
further the 4 values obtained are checked for ∆ABC .....the value which satisfies Pythagoras theorerm.... is the answer