Try this beautiful Problem on Geometry from Trapezium from (AMC 10 A, 2009).
Convex quadrilateral has
and
. Diagonals
and
intersect at
, and
and
have equal areas. What is
,
Geometry
quadrilateral
Similarity
Pre College Mathematics
AMC-10A, 2009 Problem-23
Given that Convex quadrilateral has
and
. Diagonals
and
intersect at
, and
and
have equal areas. we have to find out the length of
.
Now if we can show that and
are similar then we can find out
?
Can you find out?
Given that area of and area of
are equal. Now area of
= area of
+
Area of = area of
+
Therefore area of = area of
[as area of
and area of
are equal]
Since triangles and
share a base, they also have the same height and thus
and
with a ratio of 3: 4
Can you finish the problem?
Therefore so
Try this beautiful Problem on Geometry from Trapezium from (AMC 10 A, 2009).
Convex quadrilateral has
and
. Diagonals
and
intersect at
, and
and
have equal areas. What is
,
Geometry
quadrilateral
Similarity
Pre College Mathematics
AMC-10A, 2009 Problem-23
Given that Convex quadrilateral has
and
. Diagonals
and
intersect at
, and
and
have equal areas. we have to find out the length of
.
Now if we can show that and
are similar then we can find out
?
Can you find out?
Given that area of and area of
are equal. Now area of
= area of
+
Area of = area of
+
Therefore area of = area of
[as area of
and area of
are equal]
Since triangles and
share a base, they also have the same height and thus
and
with a ratio of 3: 4
Can you finish the problem?
Therefore so