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19, In figure, S and T trisect the side QR of a right triangle POR, prove that :S TR |
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Answer» Since, S and T trisect the side QR QS = TS = RT Let’s assume QS = TS = RT = x QR = 3x and QT = 2x In Right angled triangle PQR, PR2= PQ2+ QR2 PR2= PQ2+(3x)2 PR2= PQ2+ 9x2 In Right angled triangle PQS, PS2= PQ2+QS2 PS2= PQ2+x2 In Right angled triangle PQT, PT2= PQ2+ OT2 PT2= PQ2+ (2x)2 PT2= PQ2+ 4x2 To prove that, 8PT2=3 PR2+ 5PS2 LHS = 8PT2= 8(PQ2+ 4x2) = 8PQ2+ 32x2 RHS = 3 PR2+ 5PS2= 3(PQ2+ 9x2) – 5 (PQ2+ x2)= 3PQ2+ 27x2+ 5PQ2+ 5x2= 8PQ2+ 32x2 LHS = RHS Hence, proved |
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