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प्रश्न
In figure, if DE || BC, then `(ar(ΔADE))/(ar(DECB)` = ______.
रिकाम्या जागा भरा
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उत्तर
In figure, if DE || BC, then `(ar(ΔADE))/(ar(DECB)` = `underlinebb(1/3)`.
Explanation:
DE = 6 cm, BC = 12 cm
⇒ `(DE)/(BC) = 1/2`
DE || BC so ΔADE ∼ ΔABC; corresponding linear ratio = `1/2`.
Hence `(area(ΔADE))/(area(ΔABC)) = (1/2)^2 = 1/4`.
Area (DECB) = area (ΔABC) – area (ΔADE)
= `1 - 1/4`
= `3/4` of area (ΔABC)
Therefore `(ar(ΔADE))/(ar(DECB)) = (1/4)/(3/4) = 1/3`.
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