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 => 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
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
Jiskha idiot stupid mental fellow
Given:BC||DF, BE||BCand BCDF is rectangle.
Opp. side of rectangle are equal.