Question

In the figure, ABCDE is a pentagon with BE||CD and BC||DE. BC is perpendicular to CD. AB= 5cm, AE=5cm, BE= 7cm, BC= x-y and CD= x+y. If the perimeter of ABCDE is 27cm. find the value of x and y, given x, y ≠ 0

Answer 1

in given ABCDE Pentagon x = 6 & y = 1

Step-by-step explanation:

BE||CD and BC||DE

=> BCDE is a parallelogram

now BC is perpendicular to CD

=> BCDE is a rectangle

BC = DE = x - y

CD = BE = x + y = 7

Perimeter of pentagon

AB + BC + CD + DE + EA = 27

=> 5 + (x - y) + 7 + (x - y) + 5 = 27

=> 2(x - y) = 10

=> x - y = 5

  x + y = 7

Adding both

2x = 12

=> x = 6

& y = 1

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