Question

In the fig, ABCDE is a pentagon with BE||CD and BC||DE . BC is perpendicular to CD . If the perimeter of ABCDE is 21cm, find the values of x and y

Plz explain by telling the steps!!

Answer 1

Since BC|| DE and BE || CD with BC bisects CD, BCDE is a rectangle.
: opp sides are equal
i.e, BE = CD : x + y = 5 ......(1)
DE = BC : x - y .......(2)
Since perimeter of ABCDE is 21
: AB + BC + CD + DE + EA = 21
3 + x - y + x + y + x - y + 3 = 21
6 + 3x - y = 21
3x - y = 15
Adding (1) and (2) we get
4x = 20
x = 20/4
x = 5
Putting x = 5 in (1)
(5) + y = 5
y = 5 - 5
y = 0
: x = 5 , y = 0