ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of triangle AEB is

Options

1. 10
2. 9
3. 8
4. 7

Correct Answer

8

Explanation

By AAA similarity, △AEC ∼ △DEC: AB / DC = AE / DE = BE / CE = 2 / 1 Let: DE = x cm, CE = y cm The perimeter of △AEB: Perimeter = AB + AE + BE = 2 + 2x + 2y = 2 + 2(x + y) From the trapezium ABCD: AD + BC = 3 ⇒ x + y = 3 Substitute: Perimeter of △AEB = 2 + 2(3) = 8 cm

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