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Question
Vertices of given triangles are taken in order and their areas are provided aside. Find the value of ‘p’.
| Vertices | Area (sq.units) |
| (0, 0), (p, 8), (6, 2) | 20 |
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Solution
Let the vertices be A(0, 0) B(p, 8), c(6, 2)
Area of a triangle = 20 sq.units
`1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]` = 20
`1/2[(0 + 2"p" + 0) - (0 + 48 + 0)]` = 20
`1/2[2"p" - 48]` = 20
2p – 48 = 40
⇒ 2p = 40 + 48
p = `88/2` = 44
The value of p = 44
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