Question

In the given figure, AE || DC. If AB = 6 cm, BC = 4 cm, and AE = 9 cm, then DC is equal to ______.

Options

• 6 cm

• 5 cm

• 4 cm

• 3 cm

Answer 1

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