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Question
In the following figure, AB = 9 cm, CD = 6 cm and CM = 4 cm. Find AM.
Sum
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Solution
Given:
- ∠A = 90° and ∠C = 90°
- Line BD intersects AC at M
Similarity: △ABM ∼ △DCM
Thus, `(AB)/(CD) = (AM)/(CM)`
Substitute values:
`9/6 = (AM)/4`
`3/2 = (AM)/4`
`AM = 3/2 xx 4`
∴ AM = 6 cm
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