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प्रश्न
In the given figure, AE || DC. If AB = 6 cm, BC = 4 cm, and AE = 9 cm, then DC is equal to ______.
पर्याय
6 cm
5 cm
4 cm
3 cm
MCQ
रिकाम्या जागा भरा
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उत्तर
In the given figure, AE || DC. If AB = 6 cm, BC = 4 cm, and AE = 9 cm, then DC is equal to 6 cm.
Explanation:
Since AE || DC, and the lines AD and EC intersect at B, triangles △ABE and △DBC are similar (vertically opposite angles are equal, and corresponding angles are equal due to parallel lines).
Thus, corresponding sides are proportional:
`(AB)/(BC) = (AE)/(DC)`
Substitute the given values:
`6/4 = 9/(DC)`
`3/2 = 9/(DC)`
Cross-multiplying:
3 × DC = 2 × 9
3 × DC = 18
DC = `18/3`
∴ DC = 6 cm
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