parasmgandhi parasmgandhi

12-01-2019
Mathematics

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In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN

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sqdancefan sqdancefan

12-01-2019

Answer:

BC : BN = 8 : 3

Step-by-step explanation:

Parallel lines divide any transversal into segments with the same ratio. That means ...

... BN : NC = AM : MD = 3 : 5

Since BC = BN + NC, the desired ratio is ...

... BC : BN = (BN+NC) : BN = (3+5) : 3

... BC : BN = 8 : 3

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