# Rectangular triangle PQR

In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal places. Units "cm"

Result

p =  40.31 cm

#### Solution:

$p_{1}=\sqrt{ 20^2-16^2 }=12 \ \\ p_{2}=p_{1}+25=12+25=37 \ \\ p=\sqrt{ p_{2}^2+16^2 }=\sqrt{ 37^2+16^2 } \doteq 5 \ \sqrt{ 65 } \doteq 40.3113 \doteq 40.31 \ \text{cm}$

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