Question

The perimeter of a parallelogram ABCD is 48 cm. If BC = 3x – 2, DA = x + 2y + 2 and AB = 3y + 2, find the values of x and y.

Answer 1

Given: Parallelogram ABCD with perimeter 48 cm.

BC = 3x – 2

DA = x + 2y + 2

AB = 3y + 2

Step-wise calculation:

1. In a parallelogram, opposite sides are equal.

So, BC = DA.

Hence, 3x – 2 = x + 2y + 2.

Simplify:

3x – x = 2y + 2 + 2

⇒ 2x = 2y + 4

⇒ x = y + 2   ...(Equation 1)

2. Perimeter = 2(AB + BC) = 48

⇒ AB + BC = 24

Substitute AB and BC:

(3y + 2) + (3x − 2) = 24

⇒ 3x + 3y = 24

⇒ x + y = 8   ...(Equation 2)

3. Substitute equation 1 into equation 2:

(y + 2) + y = 8

⇒ 2y + 2 = 8

⇒ 2y = 6

⇒ y = 3

4. Then x = y + 2

= 3 + 2 

= 5