Question

in the figure below ABCDE is a Pentagon with BE||CD and BC||DE. BC is a perpendicular to CD. if the perimeter of ABCDE is 21 cm ,find the values of x and y​

Answer 1

Step-by-step explanation:

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