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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.
Solution
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`
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