Question

In ∆PQR angleQ=90° QR=b,A(∆PQR)=a
If QN perpendicular PR then show that QN=2a-b upon √b⁴+4a²

Answer 1

Given that

              PQR is a triangle and QM is perpendicular on PR

Also,

                     PR^2 - PQ^2 = QR^2

Now in traingle QMR

                                     QR^2 = QM^2+MR^2

Thus fro  above two equations for QR

 We get

                    PR^2 - PQ^2 = QM^2 + MR^2

                        QM^2 = PR^2 - PQ^2 -MR^2

                         QM^2 = (PM+MR)^2 - PQ^2 - MR^2

                           QM^2 = PM^2 + MR^2 + 2PM*MR - PQ^2 - MR^2

                            QM^2 = PM^2 + 2 PM^MR - PQ^2

                            QM^2 = PQ^2 - QM^2 + 2PM*MR - PQ^2

                           thus,         2QM^2 = 2 PM * MR

Answer 2

Answer:

Step-by-step explanation:

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