in triangle ABC , D and E are points on AB and AC also DE parallel to BC if AD =1.5 and BD = 2 AD then find
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3
Answer:
Given AD= 1.5 cm
∴BD = 3 cm and AB= AD+BD
= 1.5+3
= 4.5 cm
proof : Given , in triangle ADE and ABC
∠A is common and DE||BC.
∠ADE=∠ABC
⇒∠AED=∠ACB (corresponding angles)
∴ΔADE≅ΔABC (AA similarity)
ar(ΔABC)
ar(ΔADE)
=
AB
2
AD
2
=
(4.5)
2
(1.5)
2
=
9
1
ar(ΔABC)−ar(ΔADE)
ar(ΔADE)
=
9−1
1
∴
ar(trapeziumBCED)
ar(ΔADE)
=
8
1
solution
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