Question

Abcd is a parallelogram if ad=x+2y.Bc=2x+3.Dx=x+7.Ab=3y+2 then calculate perimeter of parallelogram

Answer 1

Opposite sides of parallelogram are equal.

Hence BC = AD

2x +3 = x + 2y

2x -x = 2y -3

x = 2y -3 (Equation 1)

AB = CD

3y + 2 = x + 7

x = 3y +2 -7

x = 3y -5( Equation 2)

Comparing 1 and 2

Hence, 2y -3 = 3y - 5

5 -3 = 3y - 2y

2 = y

Putting value of y in equation 1

x = 2y - 3

x = 2*2 -3

x = 4-3 =1

Therefore perimeter = AB +BC+CD+AD

= 3y + 2 + 2x +3 +x +7 +x + 2y

=5y +12 + 4x

= 5*2 +12 + 4*1

=10+12+4=26