Question

in the given figure BC = 4 CM, CD = 4CM,DE = 8CM, Find the ratio of the areas of angle ABC,angle ACD, angle ADE​

Answer 1

Step-by-step explanation:

Given

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

In ΔADE and ΔABC ,

∠A=∠A [Common]

∠ADE=∠ABC [Corresponding angles]

∠AED=∠ACB [Corresponding angles]

∴ΔADE∼ΔABC [AAA similarity]

Since ratio of areas of two similar triangles is equal to ratio of squares on the corresponding sides,

∴

ar(ΔABC)

ar(ΔADE)

=

(BC) 2(DE) 2

⇒ ar(ΔABC)25 = (8) 2(4) 2 = 6416 = 41Hence, ar(ΔABC)=25×4=100sq.cm