A palm tree of height 36m broke at a point P, but it did not separate. The top of the tree touched the ground at a distance of 12m from the base, find the distance of the point P from the base of the tree.
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it will forms a right triangle PQR
hence PQ+PR=36 ................. (1)
according to pythagoras theorem ,
PQ^2+QR^2=PR^2
(12)^2=PR^2-PQ^2 (QR=12, Given)
144=(PR+PQ)(PR-PQ)
Subtracting equation (2) from (1):-
2PQ=32
PQ=16m
hence PQ+PR=36 ................. (1)
according to pythagoras theorem ,
PQ^2+QR^2=PR^2
(12)^2=PR^2-PQ^2 (QR=12, Given)
144=(PR+PQ)(PR-PQ)
Subtracting equation (2) from (1):-
2PQ=32
PQ=16m
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