Question

In the adjoining figure AB, DC, EF are In parallel lines. Given that EG = 5cm, GC = 10cm, AB = 15cm, and DC = 18cm. Calculate the lengths of EF and AC.​

Answer 1

Step-by-step explanation:

In ΔEFG and ΔGCD,

∠EFG = ∠GDC (EF || CD, alt. ∠s are equal)

∠EGF = ∠CGD (vert. opp. ∠s)

∴ ΔEFG ~ ΔGCD (By AA similarity)

∴ E G G C = E F D C

⇒ E F 18 = 5 10

⇒ E F = 9 c m

EGGC=EFDC

⇒EF18=510

⇒EF=9cm

Now in Δs ABC and EFC,

∠ACB = ∠ECF (common) ∠ABC = ∠EFC (AB || EF, corr. ∠s are equal)

∴ ΔABC ~ ΔEFC (By AA similarity)

⇒ A C E C = A B E F

⇒ A C ( E G + G C ) = A B E F ACEC=ABEF

⇒AC(EG+GC)=ABEF

⇒ A C ( 5 + 10 ) = 15 9

⇒ A C = 25 c m .