Question

In the figure ab||cd. If the ratio of the perimeter of ced to that of bea is 3:2 and the sum of the perimeters if the two triangles is 110 find the perimeter of each triangle

Answer 1

the picture in the attached figure

let
x--------> perimeter of triangle CED
y--------> perimeter of triangle BEA

we know that
∠A=∠D
∠B=∠C
∠E is equal in both triangles by vertical angle
so
triangle CED and triangle BEA are similar

x+y=110------> x=110-y------> equation 1
x/y=3/2----> 2x=3y-----> equation 2

substitute equation 1 in equation 2
2*[110-y]=3y-----> 220-2y=3y----> 3y+2y=220---> 5y=220----> y=44 units
x=110-y-----> x=110-44-----> x=66 units

the answer is
perimeter of triangle CED is 66 units
perimeter of triangle BEA is 44 units