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

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(C) In a right-angled triangle,if an altitude is drawn from the right-angle vertex to the hypotenuse,the triangle on either side of the altitude is si

Vedclass · Accepted Answer

$6$

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(C) In a right-angled triangle,if an altitude is drawn from the right-angle vertex to the hypotenuse,the triangle on either side of the altitude is similar to the original triangle and to each other.Specifically,$\Delta RMQ \sim \Delta RQP$.From the property of similar triangles,the ratio of corresponding sides is equal:$\frac{RM}{RQ} = \frac{RQ}{RP}$.Given $QR = 9$ and $PR = 13.5$.Substituting the values into the equation:$\frac{RM}{9} = \frac{9}{13.5}$.$RM = \frac{9 	imes 9}{13.5}$.$RM = \frac{81}{13.5}$.$RM = 6$.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $QR = 9$ and $PR = 13.5$,find $RM$.

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