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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 |
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Answer» 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 Learn more: PERIMETERS of two similar triangles are 30cm and 40cm respectively ... Ratio of area of 2 similar triangles are 2:3. Area of the LARGER triangle is |
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