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ICSE Class 9 Answered

in triangle XYZ, angle XZY= 90 , XY = z units, YZ = x units, ZX= y units, ZDis perpendicular to XY and ZD = p units, prove that: 1 / p2 = 1 / x2 + 1 / y2
Asked by hemanginivyas92.9spicertl | 20 Aug, 2020, 09:55: PM
answered-by-expert Expert Answer
Using the formula for Area of triangle = 1/2 x Base x Height
Area of triangle XYZ = 1/2 xy
Also, Area of triangle XYZ = 1/2 pz
Therefore, 1/2 xy = 1/2 pz
xy = pz
straight p equals xy over straight z space.... space left parenthesis straight i right parenthesis As space in space triangle XYZ comma space angle XZY equals 90 degree comma space using space Pythagoras space theorem rightwards double arrow straight z squared equals straight x squared plus straight y squared From space left parenthesis straight i right parenthesis comma space we space have straight p squared equals fraction numerator straight x squared straight y squared over denominator straight z squared end fraction rightwards double arrow 1 over straight p squared equals fraction numerator straight z squared over denominator straight x squared straight y squared end fraction equals fraction numerator straight x squared plus straight y squared over denominator straight x squared straight y squared end fraction equals 1 over straight y squared plus 1 over straight x squared rightwards double arrow 1 over straight p squared equals 1 over straight x squared plus 1 over straight y squared
Answered by Renu Varma | 21 Aug, 2020, 11:59: AM

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