Question

ABCD is a parallegram if AD=x+2y, BC=2x+3,DC=x+7 and AB = 3y+2 then calculate thevperimeter of the parallelogram

Answer 1

Answer with explanation:

It is given that in Parallelogram A B CD,AD=x+2 y, BC=2 x+3,DC=x+7 and AB = 3 y+2.

Properties of parallelogram that will be used in this question

1. Opposite sides are equal.

2. Perimeter of parallelogram = Sum of length of four sides

AB=CD→3 y +2=x+7→x - 3 y= 2-7→x- 3 y= -5-----(1)

AD=BC→x + 2 y= 2 x +3→2 x -x -2 y= -3→x - 2 y= -3--------(2)

(1) -  (2)

x-3 y - x + 2 y= -5 +3

- y= -2

y=2

Substituting the value of ,y in equation (1)

x - 3 × 2= -5

x-6= -5

x=6-5

x=1

AD=x+2 y= 1 +2 ×2=1+4=5

BC=2 x+3=2 ×1+3=5

DC=x+7=1+7=8

AB = 3 y+2=3×2+2=6+2=8

→Perimeter of parallelogram A B CD= 5+8+5+8=26 units