7. In ∆ ABC, P, Q and R are the midpoints of
AB, BC and AC respectively. If AB = 8 cm,
BC = 9 cm and AC = 10.6 cm, find the perimeter
of ∆PQR.
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Answer:
REF.Image.
In △ABCAQ,BR,CP are the median.
Consider point D is at the intersections of all medians & we know by therom by median
DQ
AD
=
1
2
;
DR
BD
=
1
2
;
DP
CD
=
1
2
DA+DB+DC=2DQ+2DR+2DP
DA+DB+DC=2(DP+DQ+DR)...(i)
In △ABCP,Q,R are the midpoint
AP=
2
AB
;BQ=
2
BC
;RC=
2
AC
from the therom; the sum of the square of the median of a triangle to the sum of the square of sides.
3(AB
2
+BC
2
+AC
2
)=4(AQ
2
+BR
2
+CP
2
)
PA+QB+RC=a...(ii)
2
AB
+
2
BC
+
2
AC
=a
(AB+BC+AC)=2a...(iii)
from eq (iii) & (ii)
PA+QB+RC=
2
(AB+BC+CC)
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