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Mathematics
Problem
△
L
M
N
\triangle LMN
△
L
M
N
has points
P
P
P
on
L
M
LM
L
M
and
Q
Q
Q
on
L
N
LN
L
N
such that
P
Q
∥
M
N
PQ \parallel MN
P
Q
∥
M
N
. The ratio
L
P
:
P
M
LP:PM
L
P
:
P
M
is
3
:
5
3:5
3
:
5
. a. (i) Determine
L
Q
:
Q
N
LQ:QN
L
Q
:
QN
. b. (ii) If the perimeter of
△
L
M
N
\triangle LMN
△
L
M
N
is
72
cm
72\,\text{cm}
72
cm
and
M
N
=
18
cm
MN = 18\,\text{cm}
M
N
=
18
cm
, calculate the perimeter of
△
L
P
Q
\triangle LPQ
△
L
P
Q
. c. (iii) Find the ratio of the areas
[
△
L
P
Q
]
:
[
△
L
M
N
]
[\triangle LPQ]:[\triangle LMN]
[
△
L
P
Q
]
:
[
△
L
M
N
]
.
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