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LMT
2020 LMT Spring
14
14
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 14
Source:
8/22/2020
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle such that
A
B
=
40
AB=40
A
B
=
40
and
A
C
=
30.
AC=30.
A
C
=
30.
Points
X
X
X
and
Y
Y
Y
are on the segment
A
B
AB
A
B
and
B
C
,
BC,
BC
,
respectively such that
A
X
:
B
X
=
3
:
2
AX:BX=3:2
A
X
:
BX
=
3
:
2
and
B
Y
:
C
Y
=
1
:
4.
BY:CY=1:4.
B
Y
:
C
Y
=
1
:
4.
Given that
X
Y
=
12
,
XY=12,
X
Y
=
12
,
the area of
△
A
B
C
\triangle ABC
△
A
BC
can be written as
a
b
a\sqrt{b}
a
b
where
a
a
a
and
b
b
b
are positive integers and
b
b
b
is squarefree. Compute
a
+
b
.
a+b.
a
+
b
.