maths
posted by geometry .
ABCDE is a Pentagon with BE parallel to CD and BC parallel to DE. BC is perpendicular to CD. if the perimeter of ABCDE is 21cm. Find the value of x and y.

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 
Since BC  DE and BE  CD with B perpendicular to CD , BCDE is a rectangle
=> opp sides are equal
BE=CD => x+y=5.....(1)
DE=BC => xy
Since perimeter of ABCDE is 21
=> AB+BC+CD+DE+EA=21
3+xy+x+y+xy+3=21
6+3xy = 21
3xy = 15
xy = 5.....(2)
Adding (1) and (2) we get
2x = 10
x= 10/2
x= 5
Put x=5 in eq (1)
(5)+y=5
Y= 55
Y=0
Hence, x=5 and y=0 
Since BC  DE and BE  CD with B perpendicular to CD , BCDE is a rectangle
=> opp sides are equal
BE=CD => x+y=5.....(1)
DE=BC => xy
Since perimeter of ABCDE is 21
=> AB+BC+CD+DE+EA=21
3+xy+x+y+xy+3=21
6+3xy = 21
3xy = 15
xy = 5.....(2)
Adding (1) and (2) we get
2x = 10
x= 10/2
x= 5
Put x=5 in eq (1)
(5)+y=5
Y= 55
Y=0
Hence, x=5 and y=0 
Since BC  DE and BE  CD with B perpendicular to CD , BCDE is a rectangle
=> opp sides are equal
BE=CD => x+y=5.....(1)
DE=BC => xy
Since perimeter of ABCDE is 21
=> AB+BC+CD+DE+EA=21
3+xy+x+y+xy+3=21
6+3xy = 21
3xy = 15
xy = 5.....(2)
Adding (1) and (2) we get
2x = 10
x= 10/2
x= 5
Put x=5 in eq (1)
(5)+y=5
Y= 55
Y=0
Hence, x=5 and y=0
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