Question

In the figure DE parallel to BC. If AD = 4cm, DB = 8 cm and AC = 18 cm, find the lengths ofAE and EC.

Answer 1

Answer:

ΔABC in which DE ∥BC and DE = 4cm, BC = 8 cm. and ar. (ΔADE) = 25 sq. cm.In ΔADE and ΔABC

∠A=∠A       [Common]

∠ADE=∠ABC      [Corresponding angles]

∠ADE=∠ACB      [Corresponding angles]

∴ΔADE∼ΔABC       [AAA similarity]

Since ratio of areas of two similar Δs is equal to ratio of squares on the corresponding sides.

∴ar(ΔABC)ar(ΔADE)=(BC)2(DE)2

⇒ar(]DeltaABC)25=(8)2(4)2=6416=41

Hence, ar(ΔABC)=25×4=100sq.m