Question

In the given figure, ∠B = ∠E, ∠ACD = ∠BCE, AB = 10.4 cm and DE = 7.8 cm. Find the ratio between areas of the ∆ABC and ∆DEC.

Answer 1

Given, ∠ACD = ∠BCE

∠ACD + ∠BCD = ∠BCE + ∠BCD

∠ACB = ∠DCE

Also, given ∠B = ∠E

∴ ∆ABC ∼ ∆DEC

`(ar(ΔABC))/(ar(ΔDEC)) = ((AB)/(DE))^2`

= `(10.4/7.8)^2`

= `(4/3)^2`

= `16/9`