Question

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

Answer 1

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Hey dear!

Here is yr answer.....

Given,

pentagon ABCDE ,

Perimeter of ABCDE = 21cm


AB = 3cm
BC = x-y
CD = x+y
AE = 3cm
BE = 5cm

BE||CD, BC||DE, BC is perpendicular to CD

So, opp. sides are equal!

CD = BE

x+y = 5 ------- (1)


BC = DE = x-y


Now,

AB+BC+CD+DE+AE = 21

3+x-y+x+y+x-y+3 = 21

3x-y+6 = 21

3x-y = 21-6

3x-y = 15 -------- (2)


Now add (1) and (2)

3x-y+x+y = 15+5

4x = 20

x = 20/4

x = 5


Substitute x value in (2)

3x-y = 15

3(5)-y= 15

15-y = 15

-y = 15-15

-y = 0

y = 0


Therefore, x = 5 & y = 0




Hope it hlpz...

Answer 2

$\textbf{HELLO DEAR,}$

given that:-

AB = 3cm = AE = 3cm ,
BC = (x - y) ,
CD = (x + y) ,
BE = 5cm

in the fig, BE || CD , BC || DE , and , BC ⊥ CD,
thus, BCDE is rectangle,

hence, CD = BE = 5cm , BC = DE = (x - y)

(x + y) = 5----------( 1 )

now,

perimeter of ABCDE = AB + BC + CD + DE + AE

now, put the values of them

we get,

21 = 3 + (x - y) + (x + y) + (x - y) + 3
[ perimeter = 21 (given), ]

=> 21 = 6 + 2(x - y) + (5) ----------------from --( 1 )

=> 21 - 11 = 2(x - y)

=> 10/2 = (x - y)

=> (x - y) = 5 ----------( 2 )

from------( 1 ) & ------( 2 )

x + y = 5
x - y = 5
—————
2x = 10

x = 5 ---[ put in ---( 1 ) ]

we get,

x + y = 5

5 + y = 5

y = 5 - 5

y = 0 , x = 5

$\textbf{I HOPE ITS HELP YOU, THANKS}$