Question

In the figure, angle ADE = angle B and if AD = 3.8cm, BE=2.1 cm, BC = 4.2 cm
then DE =
A) 1.8 cm
B) 2.4 cm
C) 2.1 cm
D) 2.8 cm​

Answer 1

Answer:

From given figure,

∠ADE=∠B

To prove: ΔADE∼ΔABC and

find DE

Given: AD=3.8cm, AE=3.6cm, BE=2.1cm and BC=4.2cm

Now, In ΔADE and ΔABC

∠ADE=∠B (given)

∠A=∠A (common)

ΔADE∼ΔABC (By AA)

Again,

AD

=

BC

DE

AE+EB

AD

=

4.2

x

3.6+2.1

3.8

=

4.2

x

5.4

3.8

=

4.2

x

x=2.8

DE=2.8cm