∆ABC is a right angled triangle with B=90°. 'D' and 'E' are points on
AB and Ac respectively, such that DE II BC. If AB=9 cm, BC=12 cm, and
AD:DB=1:2, then find the length of AE.
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Length of AE = 5 cm if DE ║ BC AB = 9 cm , BC = 12 cm AD:DB = 1 : 2
Step-by-step explanation:
As DE ║ BC
=> ΔADE ≈ ΔABC
=> AD/AB = AE / AC
AD /DB = 1/2
=> DB/AD = 2
Adding 1 both sides
=> DB/AD + 1 = 2 + 1
=> (DB + AD)/AD =3
DB + AD = AB
=> AB/AD = 3
=> AD/AB = 1/3
=> AE / AC = 1/3
=> AE = AC/3
AC² = AB² + BC²
=> AC² = 9² + 12²
=> AC² = 81 + 144
=> AC² = 225
=> AC = 15
AE = AC/3 = 15/3
=> AE = 5
Length of AE = 5 cm
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