Question

In triangle PQR angle Q=90°,angle P=45° ,QR=5cm what is the length of PR?

Answer 1

40degree

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Answer 2

Given :-

• In ∆PQR, ∠Q = 90° .
• ∠P = 45° .
• QR = 5 cm.

To Find :-

• Length of PR = ?

Solution :-

In ∆PQR,

→ ∠P + ∠Q + ∠R = 180° (angle sum property of a ∆.)

→ 45° + 90° + ∠R = 180°

→ 135° + ∠R = 180°

→ ∠R = 180° - 135°

→ ∠R = 45° .

so,

→ ∠R = ∠P .

now, we know that,

• Sides opposite to equal angles are equal in length .

therefore,

→ QR = QP = 5 cm.

hence,

→ PR = √(QR² + QP²) (by pythagoras theorem.)

→ PR = √(5² + 5²)

→ PR = √(25 + 25)

→ PR = √(50)

→ PR = 5√2 cm. (Ans.)

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