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3 years ago

In the figure, BD¯¯¯¯¯ bisects ∠ABC .

Mathematics

1 answer:

pashok25 [27]3 years ago

5 0

The bisector BD is perpendicular to the line segment AC then the angle formed in between is 90°. We can solve for DC using SOH CAH TOA theorem or Pythagorean theorem.
Since ∠BDA is 90°, we can examine that AD is equal to 2units. Proving this, we have BD^2=BD^2+AD^2.
3^2=DB^2+2^2
DB=5units
Therefore, DC=AC-AD and the answer is 2 units.

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3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

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$\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.$

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Subtract the first equation from the second:

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Answer: $h=\dfrac{180}{17}\ cm.$

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