Question

in the figure ABCDE is a pentagon with BE||CD and BC||DE. BC is perpendicular to CD. AB = 5 cm, AE = 5cm, BE = 7 cm, BC = (x-y), and CD = (x + y). if the perimeter of ABCDE is 27cm. find the value of X and y, given x, y not equal to 0​

Answer 1

Answer:

x=6,y=1

Step-by-step explanation:

As in quadrilateral BCDE, opposite sides are parallel and all angles are right angles, hence BCDE is a rectangle.

We know that, opposite sides of rectangle are equal.

∴ BE = CD = 7cm

∴ x + y = 7 ………(1)

And BC = DE

∴ BC = DE = x – y ………(2)

Now, perimeter of pentagon ABCDE is

P = AB + BC + CD + DE + EA

∴ 27 = 5 + (x – y) + 7 + (x – y) + 5

∴ 27 = 17 + 2x – 2y

∴ 10 = 2x – 2y

∴ x – y = 5 ………(3)

Adding equations (1) & (3),

∴ 2x = 12

∴ x = 6

Substituting x in eq (1),

∴ 6 + y = 7

∴ y = 1