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# Q and R of a triangle PQR are 25° and 65°. Is PQR a right-angled triangle? Moreover, PQ is 4cm and PR is 3 cm. Find QR.

Answer :

In ΔPQR, ∠Q = 25° and ∠R = 65°.

__We know that sum of angles of a triangle = 180°.__

⇒ ∠P + ∠Q + ∠R = 180°

⇒ ∠P + 25° + 65° = 180°

⇒ ∠P = 180° - 90°

∴ ∠P = 90°

∴ Δ PQR is a right angled triangle which is right angled at P.

Given, PQ = 4 cm and PR = 3 cm

__We know that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.__

⇒ In ΔPQR, QR^{2} = PQ^{2} + PR^{2}

⇒ QR^{2} = 4^{2} + 3^{2}

= 16 + 9

= 25

∴ QR = √25 = 5 cm

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