Question

in a triangle ABC, points D and E respectively lie on side AB and AC such that DE II BC. If AD=6cm, DB = (12x–6) cm, AE = 2x cm and CE = 16–2x cm then what is the value of x?​

Answer 1

In a triangle ABC, points D and E respectively lie on side AB and AC such that, DE II BC. If AD=6cm, DB = (12x–6) cm, AE = 2x cm and CE = 16–2x cm then, the value of x = 2.

• Given that : AD=6cm, DB=(12-6)cm, AE=2x cm, CE=16-2x cm.

• In the triangle ABC and ADE,

angleADE = angleABC

angleAED = angleACB

and angle BAC is same for both angles.

• So, both the above triangles are congruent to each other by AAA congruency.

• Hence, all the parallel sides of both the triangles are in equal ratio.

• AB/AD = AC/AE

• 12x/6 = 16/2x

• By solving the above equation, we get-

x = 2