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 =?

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Chandra Prakash Maurya · Answer

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 PM 2 +MZ 2 =PZ 2 ( By Pythagoras theorem) (30-x) 2 + 15 2 =(x-5) 2 900+x 2 -60x+225=x 2 +25-10x 1100-50x=0 1100=50x X=1100/50=22 units Therefore PV is of length 22 units.

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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 =?

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