Question

In triangle PQR, l(PQ)=4.5cm, l(PR)=11.7cm, m angle PQR= 90 degree

Answer 1

Answer:

Given: ΔPQR is an isosceles triangle with PQ = PR and m∠PQR = 35° In ΔPQR: ∠PQR = ∠PRQ = 35° (Angle opposite to equal sides) Again, by angle sum property ∠P + ∠Q + ∠R = 180° ∠P + 35° + 35° = 180° ∠P + 70° = 180° ∠P = 180° – 70° ∠P = 110° Now, in quadrilateral SQTR, ∠QSR + ∠QTR = 180° (Opposite angles of quadrilateral) 110° + ∠QTR = 180° ∠QTR = 70°

Answer 2

Finding it by Pythagoras theorem.

[h² = b² + a² ]

where h is hypotenuse, b is base and a is altitude.

11.7 ² = 4.5 ² + a²

136.89 = 20.25 + a²

136.89 - 20.25 = a²

116.64 = a²

a = √116.64

a = 10.8 cm