Question

angle abc is a right angle triangle with Angle B equals to 90 degree D and e are points on AB and ac respectively such that De parallel BC if ab = 9 CM BC equals to 12 cm and a b is to DB equals to 1 in 1 is to 2 then find the length of AE​

Answer 1

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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