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Mathematics
Problem
A
B
C
D
ABCD
A
B
C
D
is a trapezium with parallel sides
A
B
=
a
AB = a
A
B
=
a
cm and
D
C
=
b
DC = b
D
C
=
b
cm,
E
E
E
and
F
F
F
are the mid-points of the non-parallel sides. Find the ratio of
a
r
(
A
B
F
E
)
ar(ABFE)
a
r
(
A
B
F
E
)
and
a
r
(
E
F
C
D
)
ar(EFCD)
a
r
(
E
F
C
D
)
. (A)
(
3
b
+
a
)
:
(
3
a
+
b
)
(3b + a) : (3a + b)
(
3
b
+
a
)
:
(
3
a
+
b
)
(B)
(
3
a
+
b
)
:
(
3
b
+
a
)
(3a + b) : (3b + a)
(
3
a
+
b
)
:
(
3
b
+
a
)
(C)
(
2
a
+
3
b
)
:
(
3
a
+
b
)
(2a + 3b) : (3a + b)
(
2
a
+
3
b
)
:
(
3
a
+
b
)
(D)
(
3
a
+
2
b
)
:
(
2
a
+
3
b
)
(3a + 2b) : (2a + 3b)
(
3
a
+
2
b
)
:
(
2
a
+
3
b
)
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