PQR - Euclid

Find the length of line segment PR - leg of the right triangle PQR.
PQ=17 cm
PS=15 cm
QS=8 cm;

Point S is the height touch point with a hypotenuse of the RQ.

Correct answer:

PR =  31.875 cm

Step-by-step explanation:

$$\begin{gathered} PQ=17\text{cm} \\ PS=15\text{cm} \\ QS=8\text{cm} \\ |PS{|}^2=|QS|.|SR| \\ SR=\frac{P{S}^2}{QS}=\frac{15^2}{8}=\frac{225}{8}=28.125\text{cm} \\ RQ=SR+QS=28.125+8=\frac{289}{8}=36.125\text{cm} \\ R{Q}^2=P{R}^2+R{Q}^2 \\ PR=\sqrt{R{Q}^2-P{Q}^2}=\sqrt{36.125^2-17^2}=31.875\text{cm} \end{gathered}$$

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