CAT 2024 Slot 2 QA Question 17: 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, o

Question

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, o

Accepted Answer

Since $AB$ is parallel to $CD$ and the sides $AD$ and $BC$ meet at $E$, triangles $EAB$ and $EDC$ are similar.
$\dfrac{AB}{CD} = \dfrac{EA}{ED} = \dfrac{EB}{EC} = \dfrac{2}{1}$
So, $EA = 2ED$ and $EB = 2EC$.
$AD = EA - ED = ED$
$BC = EB - EC = EC$
Given perimeter of $ABCD$ is $6$ cm:
$AB + BC + CD +

ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB=2AB = 2AB=2 cm, CD=1CD = 1CD=1 cm, and perimeter of ABCDABCDABCD is 666 cm, then the perimeter, in cm, of △AEB\triangle AEB△AEB is

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