In Delta PQR,m angle P = 90^{circ} and overli | vedclass

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(B) In a right-angled triangle $\Delta PQR$,where $\angle P = 90^{\circ}$ and $\overline{PM}$ is the altitude to the hypotenuse $\overline{QR}$,the ge

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$4x^{2}$

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(B) In a right-angled triangle $\Delta PQR$,where $\angle P = 90^{\circ}$ and $\overline{PM}$ is the altitude to the hypotenuse $\overline{QR}$,the geometric mean theorem states that the altitude to the hypotenuse is the geometric mean of the segments of the hypotenuse.Therefore,the relationship is given by $PM^{2} = QM \cdot RM$.Substituting the given values:$PM^{2} = (2x^{2}) \cdot (8x^{2})$$PM^{2} = 16x^{4}$Taking the square root of both sides:$PM = \sqrt{16x^{4}}$$PM = 4x^{2}$

In $\Delta PQR$,$m \angle P = 90^{\circ}$ and $\overline{PM}$ is an altitude. If $QM = 2x^{2}$ and $RM = 8x^{2}$,then $PM = \ldots \ldots$

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