Question

Abcde is a Pentagon with be parallel to cd and bc parallel to de . Bc is perpendicular to cd ae =5cm ,be=7cm and bc=x-y and cd=x+y if the perimeter of abcde is 27 cm .find the value of x and y given that x,y is not equal to 0​

Answer 1

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 = 0Step-by-step explanation:

Answer 2

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