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Question on triangles?
Given triangle ABD, with C on side side AD such that AC = 4 and CD = 5. Side AB = 6. Find BC if perimeter of triangle BCD is 20.
2 Answers
- PopeLv 73 years agoFavorite Answer
Let BC = 6.
Using the law of cosines, equate two expressions for cos(∠BAD).
(4² + 6² - x²) / [2(4)(6)] = [9² + 6² - (15 - x)²] / [2(9)(6)]
(52 - x²) / 4 = (-x² + 30x - 108) / 9
9(52 - x²) = 4(-x² + 30x - 108)
468 - 9x² = -4x² + 120x - 432
5x² + 120x - 900 = 0
x² + 24x - 180 = 0
(x + 30)(x - 6) = 0
x = -30 or x = 6
Reject the negative solution.
x = 6
BC = 6
