Question

In the given figure DE|| BC, find the value of x.
please answer soon ​

Answer 1

Answer:

From the figure, it is given that DE║BC and AD=(x+4)cm,DB=(x+3)cm,

AE=(2x−1)cm,EC=(x+1)cm

In ΔADE and ΔABC,we have

∠A=∠A( common)

∠EDA=∠CBA (Corresponding angles)

Hence, by AA similarity,

ΔADE is similar to ΔABC

Therefore, by similarity of triangles,

AB

AD

=

BC

DE

=

AC

AE

AD+BD

AD

=

AE+EC

AE

AD

AD+BD

=

AE

AE+EC

1+

AD

BD

=1+

AE

EC

AD

BD

=

AE

EC

Substituting the values, we have

2x+7

x+4

=

3x

2x−1

AD

BD

=

AE

EC

⇒

x+4

x+3

=

2x−1

x+1

⇒2x

2

+5x−3=x

2

+5x+4

⇒x

2

=7

⇒x=

7