Q. 2 C5.0( 1 Vote )

# Vertices of the triangles taken in order and their areas are given below. In each of the following find the value of a.

Vertices: (a, –3), (3, a), (–1,5)

Area (in sq. units): 12

Answer :

Vertices of triangle A (a, –3), B (3, a) and C (–1, 5)

Area of triangle = 12 sq. units

Area of triangle =

x_{1} = a, x_{2} = 3 and x_{3} = –1

y_{1} = –3, y_{2} = a and y_{3} = 5

⇒

⇒

⇒

⇒ 12 × 2 = a^{2} – 4a + 27

⇒24 = a^{2} – 4a + 27

⇒ a^{2} – 4a + 27 – 24 = 0

⇒ a^{2} – 4a + 3

⇒ a^{2} – 3a – a + 3 = 0

⇒ a (a – 3) – (a – 3) = 0

⇒ (a – 3) (a – 1) = 0

a – 3 = 0 or a – 1 = 0

a = 3 or a = 1

Therefore, the required vertices are (3, –3) or (1, –3)

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