Posted by **geometry** on Friday, July 11, 2014 at 10:30am.

ABCDE is a Pentagon with BE parallel to CD and BC parallel to DE. BC is perpendicular to CD. if the perimeter of ABCDE is 21cm. Find the value of x and y.

- maths -
**Reena**, Thursday, July 30, 2015 at 11:36am
Since BC|| DE and BE || CD with BC bisects CD, BCDE is a rectangle.

: opp sides are equal

i.e, BE = CD : x + y = 5 ......(1)

DE = BC : x - y .......(2)

Since perimeter of ABCDE is 21

: AB + BC + CD + DE + EA = 21

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

6 + 3x - y = 21

3x - y = 15

Adding (1) and (2) we get

4x = 20

x = 20/4

x = 5

Putting x = 5 in (1)

(5) + y = 5

y = 5 - 5

y = 0

: x = 5 , y = 0

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