In a right angled triangled ABC, if ∠ABC = 90º , AB = 6 cm, BC = 8 cm and BD is perpendicular to AC, then AD : DC is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 9 : 16.
Given that
if ∠ABC = 90º , AB = 6 cm, BC = 8 cm
BD⊥AC
As we know By Pythagoras' theorem
AC2 = AB2 + BC2
AC2 = 36 + 64 = 100
AC = 10 cm
As we know that
BD2 = AD * DC
and AB2 = AD * AC
36 = AD * 10
AD = 3.6
Now, DC = AC - AD = 10 - 3.6 = 6.4 cm
AD: DC = 3.6: 6.4 = 9: 16