In triangle ABC, D and E are two points on the sides AB and AC respectively so that DE || BC and AD/BD = 5/6. The ratio of the area of ?ABC to the area of trapezium DECB is:
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 121 : 96
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Concept |
Understanding |
Application |
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If all three angles of 2 triangles are equal, then these two triangles are similar triangles. And (Area of triangle1/ Area of triangle2) = (Side12/Side22) |
Given DE ||BC, and AD/BD = 5/6 Since DE || BC, all three angles of triangle ADE and ABC are equal. Hence, triangles ADE and ABC are similar triangles.
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Area of ∆ADE/Area of ∆ABC = (AD/AB)2 ⇒Area of ∆ADE/Area of ∆ABC = (5/(5+6))2= 25 : 121
In the figure: Area of trapezium DECB= Area of ∆ABC – Area of ∆ADE (Area of ∆ABC) : (Area of trapezium ACED) = 121 : (121– 25) = 121 : 96
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