# maths

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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.

• maths -

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

• maths -

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 => x-y

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
x-y = 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= 5-5
Y=0

Hence, x=5 and y=0

• maths -

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 => x-y

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
x-y = 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= 5-5
Y=0

Hence, x=5 and y=0

• maths -

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 => x-y

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
x-y = 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= 5-5
Y=0

Hence, x=5 and y=0