Q9
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 ∆AEB is
Answer: A
Asked: perimeter of triangle AEB.
Key idea: CD ∥ AB, so triangle EDC is similar to triangle EAB with ratio CD : AB = 1 : 2.
So ED = EA/2, i.e. D is the midpoint of EA and ED = DA. Similarly EC = CB.
Perimeter of ABCD: AB + BC + CD + DA = 2 + BC + 1 + DA = 6, so DA + BC = 3.
Perimeter of AEB = AB + EA + EB = 2 + 2·DA + 2·BC = 2 + 2 × 3 = 8.
Answer: 8 cm