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wxyz is a square of side length 30 v is a point on xy and p is apoint inside the square with pv perpendicular to xy if pw =pz=pv-5 then pv =?

wxyz is a square of side length 30 v is a point on xy and p is apoint inside the square with pv perpendicular to xy if pw =pz=pv-5 then pv =?

Grade:9

1 Answers

Chandra Prakash Maurya
15 Points
4 years ago
Let PV=x ,PW=PZ=x-5
Since, P lies on  line PV which is perpendicular to XY and also P is equidistant from W and Z
Therefore P lies on the perpendicular bisector of XY.(By first postulate of Locus)
So PV also divides WZ into2 equal parts (WXUZ is a square)
Let PV intersects WZ at M
Angle VMW=Angle VMZ=90°(PV is perpendicular bisector and also bisects WZ perpendicularly )
Therefore PM=30-x.
PZ=x-5(given)
MZ=1/2×30=15 units(WZ is bisected at M by VM)
Therefore, in right angled ∆PMZ
PM2+MZ2=PZ( By Pythagoras theorem)
(30-x)2+ 152=(x-5)2
900+x2-60x+225=x2+25-10x
1100-50x=0
1100=50x
X=1100/50=22 units
Therefore PV is of length 22 units.
 
 

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