SSC CHSL 10-Jan-2017 Shift 3 Paper

Given : AB is parallel to CD. AE = 10 cm , BC = 15 cm and ED = 15 cm
To find : EC = ?
Solution : Let EC = x cm
In ∆BAE and ∆CDE
⇒ ∠ABE = ∠DCE (Alternate interior angles)
⇒ ∠BAE = ∠CDE (Alternate interior angles)
⇒ ∠AEB = ∠CED (Vertically opposite angles)
Thus, ∆BAE ∼ ∆CDE (AAA criteria)
∴

AE

DE

=

EB

EC

⇒

10

15

=

(15−x)

x

⇒

(15−x)

X

=

2

3

⇒ 45−3x=2x
⇒ 2x+3x=5x=45
⇒ x=

45

5

=9 cm