ABCD is a trapezium in which AB||DC and AB=2DC. If the diagonals of trapezium intersect each other at a point O, find the ratio of the areas of ΔAOB and ΔCOD.

A C D O B


Answer:

4:1

Step by Step Explanation:
  1. Given: A trapezium ABCD in which AB||DC and AB=2DC. Its diagonals intersect each other at the point O.
  2. Here, we have to find the ratio of ar(ΔAOB)ar(ΔCOD)=?
  3. In ΔAOB and ΔCOD , we have AOB=COD[ Vertically opposite angles ]OAB=OCD[ Alternate interior angles ]  ΔAOBΔCOD[ By AA-similarity ]
  4. We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.   ar(ΔAOB)ar(ΔCOD)=AB2DC2=(2×DC)2DC2[ AB = 2DC ]=4×DC2DC2=41 Hence, ar(ΔAOB):ar(ΔCOD)=4:1.

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