Q.4 (1) In the following figure DE || BC, then :[Figure: Δ ABC with D on side AB and E on side AC, DE parallel to BC.](i) If DE = 4 cm, BC = 8 cm, A(Δ ADE) = 25 cm2, find A(Δ ABC).(ii) If DE : BC = 3 : 5, then find A(Δ ADE) : A(□ DBCE).

Q.4 (1) In the following figure DE || BC, then :

[Figure: Δ ABC with D on side AB and E on side AC, DE parallel to BC.]

(i) If DE = 4 cm, BC = 8 cm, A(Δ ADE) = 25 cm², find A(Δ ABC).
(ii) If DE : BC = 3 : 5, then find A(Δ ADE) : A(□ DBCE).

Doubtly Asked 24 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: (i) A(Δ ABC) = 100 cm²; (ii) A(Δ ADE) : A(□ DBCE) = 9 : 16

Since DE || BC, Δ ADE ~ Δ ABC (AA test: ∠A common, ∠ADE ≅ ∠ABC as corresponding angles).

(i) \(\dfrac{A(\Delta ADE)}{A(\Delta ABC)} = \dfrac{DE^2}{BC^2} = \dfrac{16}{64} = \dfrac14\), so A(Δ ABC) = 4 × 25 = 100 cm².

(ii) \(\dfrac{A(\Delta ADE)}{A(\Delta ABC)} = \dfrac{3^2}{5^2} = \dfrac{9}{25}\). Let A(Δ ADE) = 9k and A(Δ ABC) = 25k. Then A(□ DBCE) = 25k – 9k = 16k, so the ratio is 9 : 16.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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Q.4 (1) In the following figure DE || BC, then :[Figure: Δ ABC with D on side AB and E on side AC, DE parallel to BC.](i) If DE = 4 cm, BC = 8 cm, A(Δ ADE) = 25 cm2, find A(Δ ABC).(ii) If DE : BC = 3 : 5, then find A(Δ ADE) : A(□ DBCE).

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