In a triangle abc d and e are points on the sides ab and ac respectively. De is parallel to bc, bd=2cm and de:bc = 2:3. Find ad and ratio of triangle Ade to the quadrilateral bced
Answers
Given : In a triangle abc d and e are points on the sides ab and ac respectively. De is parallel to bc, bd=2cm and de:bc = 2:3.
To find : AD & Ratio of Area of triangle Ade to the quadrilateral bced
Solution:
DE ║ BC
=> ΔADE ≈ Δ ABC
=> AD/AB = DE/BC = AE/AC
DE/BC = 2/3
=> AD/AB = 2/3
=> AD/(AD + BD) = 2/3
=> AD/(AD + 2 ) = 2/3
=> 3AD = 2AD + 4
=> AD = 4
Ratio of Area of Similar triangle = (Ratio of sides of similar triangle )²
=> Area of ΔADE / Area of Δ ABC = (2/3)²
=> Area of ΔADE / Area of Δ ABC = 4/9
=> Area of Δ ABC = 9 * Area of ΔADE / 4
Area of quadrilateral bced = Area of Δ ABC - Area of ΔADE
=> Area of quadrilateral bced = 9 * Area of ΔADE / 4 - Area of ΔADE
=> Area of quadrilateral bced = 5 * Area of ΔADE / 4
=> Area of ΔADE / Area of quadrilateral bced = 4/5
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Answer:
Step-by-step explanation:
