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Question
In ΔABC, DE is drawn parallel to BC cutting AB in the ratio 2 : 3. Calculate:
(i) `("area"(Δ"ADE"))/("area"(Δ"ABC")`
(i) `("area"("trapeziumEDBC"))/("area"(Δ"ABC"))`
Solution
AD : DB = 2 : 3
AB
= AD + DB
= 2 + 3
= 5
(i) `("area"(Δ"ADE"))/("area"(Δ"ABC")) = "AD"^2/"AB"^2`
⇒ `("area"(Δ"ADE"))/("area"(Δ"ABC")) = (2^2)/(5^2)`
⇒ `("area"(Δ"ADE"))/("area"(Δ"ABC")) = (4)/(25)`.
(ii) `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = ("area"(Δ"ABC") - "area"(Δ"ADE"))/("area"(Δ"ABC"))`
⇒ `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = (25 - 4)/(25)`
⇒ `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = (21)/(25)`.
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