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in Triangles by (15 points)
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In the given figure, PQR is a right triangle right angled at Q and QS ⊥ PR. If PQ = 6 cm and PS = 4 cm, find QS, RS and QR.

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1 Answer

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In ΔPQR 

∠PQR = 90 [Given] 

QS⊥PR [From vertex Q to hypotenuse PR] 

∴QS= PS × SR  (i)  [By theorem] 

Now , in ΔPSQ we have 

QS= PQ2 − PS2  [By Pythagoras theorem] 

= 62 − 42 

= 36 − 16 

QS= 20

⇒ QS = 25 ​cm 

QS2 = PS × SR  (i) 

⇒ (25​)= 4 × SR 

⇒ 20/4 ​= SR 

⇒ SR = 5cm 

Now , QS⊥PR 

∴ ∠QSR = 90 

⇒ QR= QS2 + SR2 [By Pythagoras theorem] 

= (25​)+ 52 

= 20 + 25 

⇒ QR= 45 

⇒ QR = 35 ​cm 

Hence, QS = 2√5​ cm, RS = 5 cm and QR = 3√5​cm.

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