Question

In triangle abc de is parallel to bc ad=3cm,db=2cm and de = 6cm find ac

Answer 1

Given: ABC is a triangle , DE parallel BC and AD= 3 cm, DB=2 cm and DE=6 cm

To find:  AE

sol:  Since DE parallel BC

     angle ADE= angle ABC (corresponding angles)

and angle AED = angle ACB  (                "               )

Triangle ADE ≈ triangle ABC ( by AA similarity)

therefore ,  AD/AB=DE/BC=AE/AC          (1)

From (1)

AD/AB=AE/AC

2/5=x/18

2×18=5x

36=5x

x=36/5

x=7.5cm

∵ AE = 7.5 cm

Answer 2

Answer:

In ∆ABC, DE II BC, Let AC be x

Therefore, By Basic Proportionality theorem,

AD/AE = AE/AC ,

2/5 = x/18, 5x = 36, x = 36/5 , x = 7.5cm