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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 =?
Let PV=x ,PW=PZ=x-5Since, P lies on line PV which is perpendicular to XY and also P is equidistant from W and ZTherefore 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 MAngle 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 ∆PMZPM2+MZ2=PZ2 ( By Pythagoras theorem)(30-x)2+ 152=(x-5)2900+x2-60x+225=x2+25-10x1100-50x=01100=50xX=1100/50=22 unitsTherefore PV is of length 22 units.
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