Question

Find the area of triangle PQR if angle Q=90, ext. angle PRX= 135, PR =10 cm.

Answer 1

PR = 10 cm

∠Q = 90 degree

∠PRX = 135

∠PRQ = 180 - 135 = 45

∠PQR = 90 - 45 = 45

Hence the triangle is isosceles .

Area = 1/2 × base × height

Let base = x cm

height = x cm

By Pythagoras theorem :

x² + x² = 10²

⇒ 2 x² = 100

⇒ x² = 50

⇒ x = √50

⇒ x = 5√2

Area = 1/2 × 5√2 × 5√2

= 5 × 5

= 25

The area is 25 cm²

Answer 2

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Hi

Here is the answer

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